Showing 1–50 of 86 results for author: Montaño, J

The multiplicity sequence of monomial ideals

Authors: Sudipta Das, Jonathan Montaño, Aniketh Sivakumar

Abstract: We give a convex-geometric formula for the multiplicity sequence of a monomial ideal in terms of mixed volumes of polytopes constructed from its Newton polyhedron. We also construct a counterexample to a conjecture of Achilles and Manaresi proposing a different volume formula for the multiplicity sequence. Finally, we derive a mixed-volume formula for the mixed multiplicities of arbitrary monomial… ▽ More We give a convex-geometric formula for the multiplicity sequence of a monomial ideal in terms of mixed volumes of polytopes constructed from its Newton polyhedron. We also construct a counterexample to a conjecture of Achilles and Manaresi proposing a different volume formula for the multiplicity sequence. Finally, we derive a mixed-volume formula for the mixed multiplicities of arbitrary monomial ideals. △ Less

Submitted 12 August, 2026; originally announced August 2026.

Matroid correspondence

Authors: Colin Crowley, Changxin Ding, Haoxi Hu, Arvind Kumar, Jonathan Montaño, Thai Thanh Nguyen, Anna Shapiro, Noah Solomon, Botong Wang, Juliet Whidden

Abstract: Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues. A matroid correspondence defines a functor between poset categories of matroids whose morphisms are matroid quotients, and various standard functors, including deletion, contraction, free extension, truncation, intersec… ▽ More Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues. A matroid correspondence defines a functor between poset categories of matroids whose morphisms are matroid quotients, and various standard functors, including deletion, contraction, free extension, truncation, intersection, union, and pullback, arise in this way. We show that these correspondences preserve representability and algebraicity under natural hypotheses. In the polymatroid setting, we establish compatibility with multisymmetric lifts. Finally, we relate this construction to the supports of linear operators with Lorentzian symbols. △ Less

Submitted 15 July, 2026; originally announced July 2026.

Homology of Vietoris-Rips complexes of hypercube graphs via group actions

Authors: Federico Galetto, Jonathan Montaño, Zoe Wellner

Abstract: The Vietoris-Rips complex of a metric space is the simplicial complex whose faces are the subsets of points with pairwise distance bounded above by a given scale $r$. In this paper, we study Vietoris-Rips complexes on the vertex set of the $n$-dimensional hypercube equipped with the Hamming distance. These complexes are stable under the action of the automorphism group of the hypercube graph, also… ▽ More The Vietoris-Rips complex of a metric space is the simplicial complex whose faces are the subsets of points with pairwise distance bounded above by a given scale $r$. In this paper, we study Vietoris-Rips complexes on the vertex set of the $n$-dimensional hypercube equipped with the Hamming distance. These complexes are stable under the action of the automorphism group of the hypercube graph, also known as the hyperoctahedral group, which therefore acts on their homology groups. Our results completely describe the decomposition of these homology groups into irreducible representations of the hyperoctahedral group at scales $r\leqslant 3$ and $r=n-1$. △ Less

Submitted 18 June, 2026; originally announced June 2026.

Comments: 41 pages, 7 figures

MSC Class: Primary: 05E45; 05E18. Secondary: 55N31; 55T25; 55U10

AGN STORM 2. XII. Ground-Based Optical Photometry and Lag Measurements of Mrk 817

Authors: John W. Montano, Aaron J. Barth, Keith Horne, Edward M. Cackett, Gisella De Rosa, Yasaman Homayouni, Erin A. Kara, Gerard A. Kriss, Hermine Landt, Gilvan G. Apolonio, Nahum Arav, Benjamin D. Boizelle, Elena Dalla Bonta, Doron Chelouche, Maryam Dehghanian, Rick Edelson, Gary J. Ferland, Carina Fian, CHen Hu, Dragana Ilic, Michael D. Joner, Shai Kaspi, Christopher S. Kochanek, Andjelka B. Kovacevic, Collin Lewin , et al. (18 additional authors not shown)

Abstract: We present the ground-based imaging campaign and light curves of Markarian 817 as part of the multiwavelength monitoring program AGN STORM\,2. Observations were carried out over 1.4 years in \emph{uBgVriz} filters, with a median cadence of 0.4 days in \emph{g}. Reverberation lags are measured using three methods (ICCF, JAVELIN, and PyROA) with the Swift UVW2 band (1928 Å) as the reference light cu… ▽ More We present the ground-based imaging campaign and light curves of Markarian 817 as part of the multiwavelength monitoring program AGN STORM\,2. Observations were carried out over 1.4 years in \emph{uBgVriz} filters, with a median cadence of 0.4 days in \emph{g}. Reverberation lags are measured using three methods (ICCF, JAVELIN, and PyROA) with the Swift UVW2 band (1928 Å) as the reference light curve. The ICCF centroid lags range from $3.0\pm0.8$ days for the $u$ band up to $7.9\pm1.5$ days for $z$, and are consistent with a $τ\propto λ^{4/3}$ dependence, the relation expected for lamp-post reprocessing by a Shakura-Sunyaev disk. Lags measured with the other methods are systematically shorter, and deviate from a $λ^{4/3}$ power-law spectrum at long wavelengths. The lags exceed thin-disk reprocessing predictions by factors of $\sim$3-6, similar to the ``disk size discrepancy'' seen in other Seyfert galaxies. We divide the campaign into three epochs with different levels of mean luminosity and X-ray obscuring column density and find that the lags vary by as much as a factor of 2 between epochs. The intrinsic spectral energy distribution is bluer and brighter during the first third of the campaign, and the longest continuum reverberation lags are obtained during that period. These results suggest that changes in ionizing luminosity can produce large variations in continuum lags on short timescales by altering the diffuse continuum luminosity emitted by the broad-line region and/or obscuring outflow, although changes in obscuration between the central engine and broad-line region may also contribute to the lag variations. △ Less

Submitted 4 May, 2026; originally announced May 2026.

Comments: 33 pages, 11 figures, 7 tables

Quasipolynomial behavior via constructibility in multigraded algebra

Authors: Hailong Dao, Ezra Miller, Jonathan Montaño, Christopher O'Neill, Kevin Woods

Abstract: Piecewise quasipolynomial growth of Presburger counting functions combines with tame persistent homology module theory to conclude piecewise quasipolynomial behavior of constructible families of finely graded modules over constructible commutative semigroup rings. Functorial preservation of constructibility for families under local cohomology, $\operatorname{Tor}$, and $\operatorname{Ext}$ yield p… ▽ More Piecewise quasipolynomial growth of Presburger counting functions combines with tame persistent homology module theory to conclude piecewise quasipolynomial behavior of constructible families of finely graded modules over constructible commutative semigroup rings. Functorial preservation of constructibility for families under local cohomology, $\operatorname{Tor}$, and $\operatorname{Ext}$ yield piecewise quasipolynomial, quasilinear, or quasiconstant growth statements for length of local cohomology, $a$-invariants, regularity, depth; length of $\operatorname{Tor}$ and Betti numbers; length of $\operatorname{Ext}$ and Bass numbers; associated primes via $v$-invariants; and extended degrees, including the usual degree, Hilbert-Samuel multiplicity, arithmetic degree, and homological degree. △ Less

Submitted 31 December, 2025; v1 submitted 20 December, 2025; originally announced December 2025.

Enhanced One-Color-Two-Photon Resonant Ionization in Highly Charged Ions by Fine-Structure Effects

Authors: Moto Togawa, Chunhai Lyu, Chintan Shah, Marc Botz, Joschka Goes, Jonas Danisch, Marleen Maxton, Kai Köbnick, Filipe Grilo, Pedro Amaro, Katharina Kubicek, Mohammed Sekkal, Awad Mohamed, Rebecca Boll, Alberto De Fanis, Simon Dold, Tommaso Mazza, Jacobo Montano, Nils Rennhack, Björn Senfftleben, Sergey Usenko, Zoltan Harman, Christoph H. Keitel, Maurice Leutenegger, Michael Meyer , et al. (3 additional authors not shown)

Abstract: Ultraintense pulses from X-ray free-electron lasers can drive, within femtoseconds, multiple processes in the inner shells of atoms and molecules in all phases of matter. The ensuing complex ionization pathways of outer-shell electrons from the neutral to the final highly charged states make a comparison with theory enormously difficult. We resolve these pathways by preparing highly charged ions i… ▽ More Ultraintense pulses from X-ray free-electron lasers can drive, within femtoseconds, multiple processes in the inner shells of atoms and molecules in all phases of matter. The ensuing complex ionization pathways of outer-shell electrons from the neutral to the final highly charged states make a comparison with theory enormously difficult. We resolve these pathways by preparing highly charged ions in an electron beam ion trap before exposing them to the pulsed radiation. This reveals how relativistic fine-structure effects shift electronic energies, largely compensate the core-screening potential, and enable the consecutive, resonant absorption of two quasi-monochromatic X-ray photons that would generally be unfeasible. This doubly-resonant channel enhances the efficiency of two-photon ionization by more than two orders of magnitude, dominating in this regime the nonlinear interaction of light and matter with possible application for future precision X-ray metrology. △ Less

Submitted 7 November, 2025; originally announced November 2025.

AGN STORM 2. XI. Spectroscopic reverberation mapping of the hot dust in Mrk 817

Authors: Hermine Landt, Benjamin D. Boizelle, Michael S. Brotherton, Laura Ferrarese, Travis Fischer, Varoujan Gorjian, Michael D. Joner, Daniel Kynoch, Jacob N. McLane, Jake A. J. Mitchell, John W. Montano, Rogemar A. Riffel, David Sanmartim, Thaisa Storchi-Bergmann, Martin J. Ward, Aaron J. Barth, Edward M. Cackett, Gisella De Rosa, Rick Edelson, Jonathan Gelbord, Yasaman Homayouni, Keith Horne, Erin A. Kara, Gerard A. Kriss, Nahum Arav , et al. (19 additional authors not shown)

Abstract: The AGN Space Telescope and Optical Reverberation Mapping 2 (STORM 2) campaign targeted Mrk 817 with intensive multi-wavelength monitoring and found its soft X-ray emission to be strongly absorbed. We present results from 157 near-IR spectra with an average cadence of a few days. Whereas the hot dust reverberation signal as tracked by the continuum flux does not have a clear response, we recover a… ▽ More The AGN Space Telescope and Optical Reverberation Mapping 2 (STORM 2) campaign targeted Mrk 817 with intensive multi-wavelength monitoring and found its soft X-ray emission to be strongly absorbed. We present results from 157 near-IR spectra with an average cadence of a few days. Whereas the hot dust reverberation signal as tracked by the continuum flux does not have a clear response, we recover a dust reverberation radius of $\sim 90$ light-days from the blackbody dust temperature light-curve. This radius is consistent with previous photometric reverberation mapping results when Mrk 817 was in an unobscured state. The heating/cooling process we observe indicates that the inner limit of the dusty torus is set by a process other than sublimation, rendering it a luminosity-invariant `dusty wall' of a carbonaceous composition. Assuming thermal equilibrium for dust optically thick to the incident radiation, we derive a luminosity of $\sim 6 \times 10^{44}$ erg s$^{-1}$ for the source heating it. This luminosity is similar to that of the obscured spectral energy distribution, assuming a disk with an Eddington accretion rate of $\dot{m} \sim 0.2$. Alternatively, the dust is illuminated by an unobscured lower luminosity disk with $\dot{m} \sim 0.1$, which permits the UV/optical continuum lags in the high-obscuration state to be dominated by diffuse emission from the broad-line region. Finally, we find hot dust extended on scales $> 140-350$ pc, associated with the rotating disk of ionised gas we observe in spatially-resolved [SIII] $λ9531$ images. Its likely origin is in the compact bulge of the barred spiral host galaxy, where it is heated by a nuclear starburst. △ Less

Submitted 24 October, 2025; originally announced October 2025.

Comments: accepted by ApJ

Measuring General Associations in Time Series: An Adaptation and Empirical Evaluation of the CODEC Coefficient in Determining Autoregressive Dynamics

Authors: Juan Pablo Montaño, Mario E. Arrieta-Prieto

Abstract: Identifying the number of lags to include in an autoregressive model remains an open research problem due to the computational burden of treating it as a hyperparameter, especially in complex models. This study explores model-agnostic association measures, including Pearson, Spearman, and an adaptation of the recently proposed conditional dependence coefficient (CODEC), for guiding lag selection i… ▽ More Identifying the number of lags to include in an autoregressive model remains an open research problem due to the computational burden of treating it as a hyperparameter, especially in complex models. This study explores model-agnostic association measures, including Pearson, Spearman, and an adaptation of the recently proposed conditional dependence coefficient (CODEC), for guiding lag selection in time series. We adapt and implement the CODEC-based Feature Ordering by Conditional Independence (CODEC-FOCI) algorithm and evaluate its performance through extensive simulations across linear, nonlinear, stationary, nonstationary, seasonal, and heteroskedastic processes. Results show that CODEC outperforms classical correlation-based measures in nonlinear and nonstationary settings, especially for large sample sizes. In contrast, Pearson performs better in purely linear models. Applications to benchmark datasets confirm that the CODEC approach identifies lag structures consistent with those reported in the literature. These findings highlight CODEC's potential as a practical, model-free tool for exploratory lag identification in time series analysis. △ Less

Submitted 7 September, 2025; originally announced September 2025.

Comments: 21 pages, 10 figures. Uses standard LaTeX math commands supported by MathJax

MSC Class: (Primary) 62M10; 62G05 (Secondary) ACM Class: G.3

Degree functions of graded families of ideals

Authors: Steven Dale Cutkosky, Jonathan Montaño

Abstract: We express multiplicities and degree functions of graded families of $\mathfrak{m}_R$-primary ideals in an excellent normal local ring $(R,\mathfrak{m}_R)$ as limits of intersection products. Moreover, in dimension 2, we show more refined results for divisorial filtrations. Finally, also in dimension 2, we give an example of a non-Noetherian divisorial filtration $\{I_n\}_{n\geqslant 0}$ of… ▽ More We express multiplicities and degree functions of graded families of $\mathfrak{m}_R$-primary ideals in an excellent normal local ring $(R,\mathfrak{m}_R)$ as limits of intersection products. Moreover, in dimension 2, we show more refined results for divisorial filtrations. Finally, also in dimension 2, we give an example of a non-Noetherian divisorial filtration $\{I_n\}_{n\geqslant 0}$ of $\mathfrak{m}_R$-primary ideals such that the union of all the sets of Rees valuations of all the $I_n$ is a finite set, and another example of a (necessarily non-Noetherian) divisorial filtration of $\mathfrak{m}_R$-primary ideals such that the set of all Rees valuations is infinite. △ Less

Submitted 5 June, 2025; originally announced June 2025.

Multiplicities and degree functions in local rings via intersection products

Authors: Steven Dale Cutkosky, Jonathan Montaño

Abstract: We prove a theorem on the intersection theory over a Noetherian local ring $R$, which gives a new proof of a classical theorem of Rees about degree functions. To obtain this, we define an intersection product on schemes that are proper and birational over such rings $R$, using the theory of rational equivalence developed by Thorup, and the Snapper-Mumford-Kleiman intersection theory for proper sch… ▽ More We prove a theorem on the intersection theory over a Noetherian local ring $R$, which gives a new proof of a classical theorem of Rees about degree functions. To obtain this, we define an intersection product on schemes that are proper and birational over such rings $R$, using the theory of rational equivalence developed by Thorup, and the Snapper-Mumford-Kleiman intersection theory for proper schemes over an Artinian local ring. Our development of this product is essentially self-contained. As a central component of the proof of our main theorem, we extend to arbitrary Noetherian local rings a formula by Ramanujam that computes Hilbert-Samuel multiplicities. In the final section, we express mixed multiplicities in terms of intersection theory and conclude from this that they satisfy a certain multilinearity condition. Then we interpret some theorems of Rees and Sharp and of Teissier about mixed multiplicities over $2$-dimensional excellent local rings in terms of our intersection product. △ Less

Submitted 26 March, 2025; v1 submitted 18 March, 2025; originally announced March 2025.

Safe Explicable Policy Search

Authors: Akkamahadevi Hanni, Jonathan Montaño, Yu Zhang

Abstract: When users work with AI agents, they form conscious or subconscious expectations of them. Meeting user expectations is crucial for such agents to engage in successful interactions and teaming. However, users may form expectations of an agent that differ from the agent's planned behaviors. These differences lead to the consideration of two separate decision models in the planning process to generat… ▽ More When users work with AI agents, they form conscious or subconscious expectations of them. Meeting user expectations is crucial for such agents to engage in successful interactions and teaming. However, users may form expectations of an agent that differ from the agent's planned behaviors. These differences lead to the consideration of two separate decision models in the planning process to generate explicable behaviors. However, little has been done to incorporate safety considerations, especially in a learning setting. We present Safe Explicable Policy Search (SEPS), which aims to provide a learning approach to explicable behavior generation while minimizing the safety risk, both during and after learning. We formulate SEPS as a constrained optimization problem where the agent aims to maximize an explicability score subject to constraints on safety and a suboptimality criterion based on the agent's model. SEPS innovatively combines the capabilities of Constrained Policy Optimization and Explicable Policy Search to introduce the capability of generating safe explicable behaviors to domains with continuous state and action spaces, which is critical for robotic applications. We evaluate SEPS in safety-gym environments and with a physical robot experiment to show its efficacy and relevance in human-AI teaming. △ Less

Submitted 25 September, 2025; v1 submitted 10 March, 2025; originally announced March 2025.

AGN STORM 2: X. The origin of the interband continuum delays in Mrk 817

Authors: Hagai Netzer, Michael R. Goad, Aaron J. Barth, Edward M. Cackett, Keith Horne, Chen Hu, Erin Kara, Kirk T. Korista, Gerard A. Kriss, Collin Lewin, John Montano, Nahum Arav, Ehud Behar, Michael S. Brotherton, Doron Chelouche, Gisella de Rosa, Elena Dalla Bonta, Maryam Dehghanian, Gary J. Ferland, Carina Fian, Yasaman Homayouni, Dragana Ilic, Shai Kaspi, Andjelka B. Kovacevic, Hermine Landt , et al. (4 additional authors not shown)

Abstract: The local (z=0.0315) AGN Mrk 817, was monitored over more than 500 days with space-borne and ground-based instruments as part of a large international campaign AGN STORM 2. Here, we present a comprehensive analysis of the broad-band continuum variations using detailed modeling of the broad line region (BLR), several types of disk winds classified by their optical depth, and new numerical simulatio… ▽ More The local (z=0.0315) AGN Mrk 817, was monitored over more than 500 days with space-borne and ground-based instruments as part of a large international campaign AGN STORM 2. Here, we present a comprehensive analysis of the broad-band continuum variations using detailed modeling of the broad line region (BLR), several types of disk winds classified by their optical depth, and new numerical simulations. We find that diffuse continuum (DC) emission, with additional contributions from strong and broad emission lines, can explain the continuum lags observed in this source during high and low luminosity phases. Disk illumination by the variable X-ray corona contributes only a small fraction of the observed continuum lags. Our BLR models assume radiation pressure-confined clouds distributed over a distance of 2-122 light days. We present calculated mean-emissivity radii of many emission lines, and DC emission, and suggest a simple, transfer-function-dependent method that ties them to cross-correlation lag determinations. We do not find clear indications for large optical depth winds but identify the signature of lower column density winds. In particular, we associate the shortest observed continuum lags with a combination of tau(1 Ryd) approx. 2 wind and a partly shielded BLR. Even smaller optical depth winds may be associated with X-ray absorption features and with noticeable variations in the width and lags of several high ionization lines like HeII and CIV. Finally, we demonstrate the effect of torus dust emission on the observed lags in the i and z bands. △ Less

Submitted 6 October, 2024; v1 submitted 3 October, 2024; originally announced October 2024.

Comments: 23 pages, 18 figures. Corrected typographical error in the title of the paper as it appeared in the Metadata

AGN STORM 2. VII. A Frequency-resolved Map of the Accretion Disk in Mrk 817: Simultaneous X-ray Reverberation and UVOIR Disk Reprocessing Time Lags

Authors: Collin Lewin, Erin Kara, Aaron J. Barth, Edward M. Cackett, Gisella De Rosa, Yasaman Homayouni, Keith Horne, Gerard A. Kriss, Hermine Landt, Jonathan Gelbord, John Montano, Nahum Arav, Misty C. Bentz, Benjamin D. Boizelle, Elena Dalla Bontà, Michael S. Brotherton, Maryam Dehghanian, Gary J. Ferland, Carina Fian, Michael R. Goad, Juan V. Hernández Santisteban, Dragana Ilić, Jelle Kaastra, Shai Kaspi, Kirk T. Korista , et al. (13 additional authors not shown)

Abstract: X-ray reverberation mapping is a powerful technique for probing the innermost accretion disk, whereas continuum reverberation mapping in the UV, optical, and infrared (UVOIR) reveals reprocessing by the rest of the accretion disk and broad-line region (BLR). We present the time lags of Mrk 817 as a function of temporal frequency measured from 14 months of high-cadence monitoring from Swift and gro… ▽ More X-ray reverberation mapping is a powerful technique for probing the innermost accretion disk, whereas continuum reverberation mapping in the UV, optical, and infrared (UVOIR) reveals reprocessing by the rest of the accretion disk and broad-line region (BLR). We present the time lags of Mrk 817 as a function of temporal frequency measured from 14 months of high-cadence monitoring from Swift and ground-based telescopes, in addition to an XMM-Newton observation, as part of the AGN STORM 2 campaign. The XMM-Newton lags reveal the first detection of a soft lag in this source, consistent with reverberation from the innermost accretion flow. These results mark the first simultaneous measurement of X-ray reverberation and UVOIR disk reprocessing lags$\unicode{x2013}$effectively allowing us to map the entire accretion disk surrounding the black hole. Similar to previous continuum reverberation mapping campaigns, the UVOIR time lags arising at low temporal frequencies are longer than those expected from standard disk reprocessing by a factor of 2-3. The lags agree with the anticipated disk reverberation lags when isolating short-timescale variability, namely timescales shorter than the H$β$ lag. Modeling the lags requires additional reprocessing constrained at a radius consistent with the BLR size scale inferred from contemporaneous H$β$-lag measurements. When we divide the campaign light curves, the UVOIR lags show substantial variations, with longer lags measured when obscuration from an ionized outflow is greatest. We suggest that, when the obscurer is strongest, reprocessing by the BLR elongates the lags most significantly. As the wind weakens, the lags are dominated by shorter accretion disk lags. △ Less

Submitted 13 September, 2024; originally announced September 2024.

Comments: 28 pages, 11 figures, 3 tables. Accepted for publication in the Astrophysical Journal

Journal ref: ApJ 974 271 (2024)

Transmission spectroscopy of CF$_4$ molecules in intense x-ray fields

Authors: Rui Jin, Adam Fouda, Alexander Magunia, Yeonsig Nam, Marc Rebholz, Alberto De Fanis, Kai Li, Gilles Doumy, Thomas M. Baumann, Michael Straub, Sergey Usenko, Yevheniy Ovcharenko, Tommaso Mazza, Jacobo Montaño, Marcus Agåker, Maria Novella Piancastelli, Marc Simon, Jan-Erik Rubensson, Michael Meyer, Linda Young, Christian Ott, Thomas Pfeifer

Abstract: The nonlinear interaction of x-rays with matter is at the heart of understanding and controlling ultrafast molecular dynamics from an atom-specific viewpoint, providing new scientific and analytical opportunities to explore the structure and dynamics of small quantum systems. At increasingly high x-ray intensity, the sensitivity of ultrashort x-ray pulses to specific electronic states and emerging… ▽ More The nonlinear interaction of x-rays with matter is at the heart of understanding and controlling ultrafast molecular dynamics from an atom-specific viewpoint, providing new scientific and analytical opportunities to explore the structure and dynamics of small quantum systems. At increasingly high x-ray intensity, the sensitivity of ultrashort x-ray pulses to specific electronic states and emerging short-lived transient intermediates is of particular relevance for our understanding of fundamental multi-photon absorption processes. In this work, intense x-ray free-electron laser (XFEL) pulses at the European XFEL (EuXFEL) are combined with a gas cell and grating spectrometer for a high-intensity transmission spectroscopy study of multiphoton-induced ultrafast molecular fragmentation dynamics in CF$_4$. This approach unlocks the direct intra-pulse observation of transient fragments, including neutral atoms, by their characteristic absorption lines in the transmitted broad-band x-ray spectrum. The dynamics with and without initially producing fluorine K-shell holes are studied by tuning the central photon energy. The absorption spectra are measured at different FEL intensities to observe nonlinear effects. Transient isolated fluorine atoms and ions are spectroscopically recorded within the ultrashort pulse duration of few tens of femtoseconds. An isosbestic point that signifies the correlated transition between intact neutral CF$_4$ molecules and charged atomic fragments is observed near the fluorine K-edge. The dissociation dynamics and the multiphoton absorption-induced dynamics encoded in the spectra are theoretically interpreted. Overall, this study demonstrates the potential of high-intensity x-ray transmission spectroscopy to study ultrafast molecular dynamics with sensitivity to specific intermediate species and their electronic structure. △ Less

Submitted 5 July, 2024; originally announced July 2024.

Comments: 30 pages, with 7 figures, submitted to Phys. Rev. X

AGN STORM 2: IX. Studying the Dynamics of the Ionized Obscurer in Mrk 817 with High-resolution X-ray Spectroscopy

Authors: Fatima Zaidouni, Erin Kara, Peter Kosec, Missagh Mehdipour, Daniele Rogantini, Gerard A. Kriss, Ehud Behar, Jelle Kaastra, Aaron J. Barth, Edward M. Cackett, Gisella De Rosa, Yasaman Homayouni, Keith Horne, Hermine Landt, Nahum Arav, Misty C. Bentz, Michael S. Brotherton, Elena Dalla Bontà, Maryam Dehghanian, Gary J. Ferland, Carina Fian, Jonathan Gelbord, Michael R. Goad, Diego H. González Buitrago, Catherine J. Grier , et al. (23 additional authors not shown)

Abstract: We present the results of the XMM-Newton and NuSTAR observations taken as part of the ongoing, intensive multi-wavelength monitoring program of the Seyfert 1 galaxy Mrk 817 by the AGN Space Telescope and Optical Reverberation Mapping 2 (AGN STORM 2) Project. The campaign revealed an unexpected and transient obscuring outflow, never before seen in this source. Of our four XMM-Newton/NuSTAR epochs,… ▽ More We present the results of the XMM-Newton and NuSTAR observations taken as part of the ongoing, intensive multi-wavelength monitoring program of the Seyfert 1 galaxy Mrk 817 by the AGN Space Telescope and Optical Reverberation Mapping 2 (AGN STORM 2) Project. The campaign revealed an unexpected and transient obscuring outflow, never before seen in this source. Of our four XMM-Newton/NuSTAR epochs, one fortuitously taken during a bright X-ray state has strong narrow absorption lines in the high-resolution grating spectra. From these absorption features, we determine that the obscurer is in fact a multi-phase ionized wind with an outflow velocity of $\sim$5200 km s$^{-1}$, and for the first time find evidence for a lower ionization component with the same velocity observed in absorption features in the contemporaneous HST spectra. This indicates that the UV absorption troughs may be due to dense clumps embedded in diffuse, higher ionization gas responsible for the X-ray absorption lines of the same velocity. We observe variability in the shape of the absorption lines on timescales of hours, placing the variable component at roughly 1000 $R_g$ if attributed to transverse motion along the line of sight. This estimate aligns with independent UV measurements of the distance to the obscurer suggesting an accretion disk wind at the inner broad line region. We estimate that it takes roughly 200 days for the outflow to travel from the disk to our line of sight, consistent with the timescale of the outflow's column density variations throughout the campaign. △ Less

Submitted 24 June, 2024; originally announced June 2024.

Clifford Theory: A Geometrical Interpretation of Multivectorial Apparent Power

Authors: M. Castilla, Juan Carlos Bravo, M. Ordoñez, Juan Carlos Montaño

Abstract: In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA) is proposed. This powerful tool permits, in n-sinusoidal/nonlinear situations, representing and calculating the voltage, current, and apparent power in a single-port electrical network in terms of multivectors. The new expressions… ▽ More In this paper, a generalization of the concept of electrical power for periodic current and voltage waveforms based on a new generalized complex geometric algebra (GCGA) is proposed. This powerful tool permits, in n-sinusoidal/nonlinear situations, representing and calculating the voltage, current, and apparent power in a single-port electrical network in terms of multivectors. The new expressions result in a novel representation of the apparent power, similar to the Steinmetz's phasor model, based on complex numbers, but limited to the purely sinusoidal case. The multivectorial approach presented is based on the frequency-domain decomposition of the apparent power into three components: the real part and the imaginary part of the complex-scalar associated to active and reactive power respectively, and distortion power, associated to the complex-bivector. A geometrical interpretation of the multivectorial components of apparent power is discussed. Numerical examples illustrate the clear advantages of the suggested approach. △ Less

Submitted 20 February, 2024; originally announced February 2024.

Comments: 10 pages, 7 figures

Journal ref: IEEE Transactions on Circuits and Systems I-Regular Papers, ( Volume: 55, Issue: 10, November 2008)

Rational powers, invariant ideals, and the summation formula

Authors: Sankhaneel Bisui, Sudipta Das, Tài Huy Hà, Jonathan Montaño

Abstract: We provide explicit descriptions for the rational powers and Rees valuations of several classes of ideals invariant under natural actions of tori and products of general linear groups, in terms of polyhedra and lattice points. This allows us to show that a version of Mustaţă-Takagi's summation formula for multiplier ideals also holds for the rational powers of these ideals. Moreover, for arbitrary… ▽ More We provide explicit descriptions for the rational powers and Rees valuations of several classes of ideals invariant under natural actions of tori and products of general linear groups, in terms of polyhedra and lattice points. This allows us to show that a version of Mustaţă-Takagi's summation formula for multiplier ideals also holds for the rational powers of these ideals. Moreover, for arbitrary ideals in normal domains that are finitely generated over algebraically closed fields, we prove a weaker version of this formula that holds for sufficiently large rational numbers. △ Less

Submitted 6 April, 2025; v1 submitted 19 February, 2024; originally announced February 2024.

Disturbance Ratio for Optimal Multi-Event Classification in Power Distribution Networks

Authors: M. D. Borrás, J. C. Bravo, J. C. Montaño

Abstract: This paper presents an effective approach to identify power quality events based on IEEE Std 1159-2009 caused by intermittent power sources like those of renewable energy. An efficient characterization of these disturbances is granted by the use of two useful wavelet based indices. For this purpose, a wavelet-based Global Disturbance Ratio index (GDR), defined through its instantaneous precursor (… ▽ More This paper presents an effective approach to identify power quality events based on IEEE Std 1159-2009 caused by intermittent power sources like those of renewable energy. An efficient characterization of these disturbances is granted by the use of two useful wavelet based indices. For this purpose, a wavelet-based Global Disturbance Ratio index (GDR), defined through its instantaneous precursor (Instantaneous Transient Disturbance index ITD(t)), is used in power distribution networks (PDN) under steady-state and/or transient conditions. An intelligent disturbance classification is done using a Support Vector Machine (SVM) with a minimum input vector based on the GDR index. The effectiveness of the proposed technique is validated using a real-time experimental system with single events and multi-events signals. △ Less

Submitted 18 February, 2024; originally announced February 2024.

Comments: 8 pages, 6 figures

Intensive Swift and LCO monitoring of PG 1302$-$102: AGN disk reverberation mapping of a supermassive black hole binary candidate

Authors: Tingting Liu, Rick Edelson, Juan V. Hernández Santisteban, Erin Kara, John Montano, Jonathan Gelbord, Keith Horne, Aaron J. Barth, Edward M. Cackett, David L. Kaplan

Abstract: We present an intensive multiwavelength monitoring campaign of the quasar PG 1302$-$102 with Swift and the Las Cumbres Observatory network telescopes. At $z\sim0.3$, it tests the limits of the reverberation mapping (RM) technique in probing the accretion disk around a supermassive black hole (SMBH) and extends the parameter space to high masses and high accretion rates. This is also the first time… ▽ More We present an intensive multiwavelength monitoring campaign of the quasar PG 1302$-$102 with Swift and the Las Cumbres Observatory network telescopes. At $z\sim0.3$, it tests the limits of the reverberation mapping (RM) technique in probing the accretion disk around a supermassive black hole (SMBH) and extends the parameter space to high masses and high accretion rates. This is also the first time the RM technique has been applied to test disk structures predicted in the SMBH binary model that has been suggested for this source. PG 1302$-$102 was observed at a $\sim$daily cadence for $\sim 9$ months in 14 bands spanning from X-ray to UV and optical wavelengths, and it shows moderate to significant levels of variability correlated between wavelengths. We measure the inter-band time lags which are consistent with a $τ\propto λ^{4/3}$ relation as expected from standard disk reprocessing, albeit with large errors. The disk size implied by the lag spectrum is consistent with the expected disk size for its black hole mass within uncertainties. While the source resembles other reverberation-mapped AGN in many respects, and we do not find evidence supporting the prevalent hypothesis that it hosts an SMBH binary, we demonstrate the feasibility of studying SMBH binaries from this novel angle and suggest possibilities for the LSST Deep Drilling Fields. △ Less

Submitted 25 January, 2024; originally announced January 2024.

Comments: 11 pages, 5 figures, 4 tables. Accepted for publication in ApJ. The full dataset will be available with the ApJ article

AGN STORM 2. VI. Mapping Temperature Fluctuations in the Accretion Disk of Mrk 817

Authors: Jack M. M. Neustadt, Christopher S. Kochanek, John Montano, Jonathan Gelbord, Aaron J. Barth, Gisella De Rosa, Gerard A. Kriss, Edward M. Cackett, Keith Horne, Erin A. Kara, Hermine Landt, Hagai Netzer, Nahum Arav, Misty C. Bentz, Elena Dalla Bonta, Maryam Dehghanian, Pu Du, Rick Edelson, Gary J. Ferland, Carina Fian, Travis Fischer, Michael R. Goad, Diego H. Gonzalez Buitrago, Varoujan Gorjian, Catherine J. Grier , et al. (27 additional authors not shown)

Abstract: We fit the UV/optical lightcurves of the Seyfert 1 galaxy Mrk 817 to produce maps of the accretion disk temperature fluctuations $δT$ resolved in time and radius. The $δT$ maps are dominated by coherent radial structures that move slowly ($v \ll c$) inwards and outwards, which conflicts with the idea that disk variability is driven only by reverberation. Instead, these slow-moving temperature fluc… ▽ More We fit the UV/optical lightcurves of the Seyfert 1 galaxy Mrk 817 to produce maps of the accretion disk temperature fluctuations $δT$ resolved in time and radius. The $δT$ maps are dominated by coherent radial structures that move slowly ($v \ll c$) inwards and outwards, which conflicts with the idea that disk variability is driven only by reverberation. Instead, these slow-moving temperature fluctuations are likely due to variability intrinsic to the disk. We test how modifying the input lightcurves by smoothing and subtracting them changes the resulting $δT$ maps and find that most of the temperature fluctuations exist over relatively long timescales ($\sim$100s of days). We show how detrending AGN lightcurves can be used to separate the flux variations driven by the slow-moving temperature fluctuations from those driven by reverberation. We also simulate contamination of the continuum emission from the disk by continuum emission from the broad line region (BLR), which is expected to have spectral features localized in wavelength, such as the Balmer break contaminating the $U$ band. We find that a disk with a smooth temperature profile cannot produce a signal localized in wavelength and that any BLR contamination should appear as residuals in our model lightcurves. Given the observed residuals, we estimate that only $\sim$20% of the variable flux in the $U$ and $u$ lightcurves can be due to BLR contamination. Finally, we discus how these maps not only describe the data, but can make predictions about other aspects of AGN variability. △ Less

Submitted 2 October, 2023; originally announced October 2023.

Comments: 23 pages, 18 figures, submitting to ApJ, comments welcome

AGN STORM 2: V. Anomalous Behavior of the CIV Light Curve in Mrk 817

Authors: Y. Homayouni, Gerard A. Kriss, Gisella De Rosa, Rachel Plesha, Edward M. Cackett, Michael R. Goad, Kirk T. Korista, Keith Horne, Travis Fischer, Tim Waters, Aaron J. Barth, Erin A. Kara, Hermine Landt, Nahum Arav, Benjamin D. Boizelle, Misty C. Bentz, Michael S. Brotherton, Doron Chelouche, Elena Dalla Bonta, Maryam Dehghanian, Pu Du, Gary J. Ferland, Carina Fian, Jonathan Gelbord, Catherine J. Grier , et al. (27 additional authors not shown)

Abstract: An intensive reverberation mapping campaign on the Seyfert 1 galaxy Mrk817 using the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST) revealed significant variations in the response of the broad UV emission lines to fluctuations in the continuum emission. The response of the prominent UV emission lines changes over a $\sim$60-day duration, resulting in distinctly different tim… ▽ More An intensive reverberation mapping campaign on the Seyfert 1 galaxy Mrk817 using the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST) revealed significant variations in the response of the broad UV emission lines to fluctuations in the continuum emission. The response of the prominent UV emission lines changes over a $\sim$60-day duration, resulting in distinctly different time lags in the various segments of the light curve over the 14 months observing campaign. One-dimensional echo-mapping models fit these variations if a slowly varying background is included for each emission line. These variations are more evident in the CIV light curve, which is the line least affected by intrinsic absorption in Mrk817 and least blended with neighboring emission lines. We identify five temporal windows with distinct emission line response, and measure their corresponding time delays, which range from 2 to 13 days. These temporal windows are plausibly linked to changes in the UV and X-ray obscuration occurring during these same intervals. The shortest time lags occur during periods with diminishing obscuration, whereas the longest lags occur during periods with rising obscuration. We propose that the obscuring outflow shields the ultraviolet broad lines from the ionizing continuum. The resulting change in the spectral energy distribution of the ionizing continuum, as seen by clouds at a range of distances from the nucleus, is responsible for the changes in the line response. △ Less

Submitted 5 January, 2024; v1 submitted 1 August, 2023; originally announced August 2023.

Comments: 20 pages, 8 figures, Accepted for publication in ApJ

AGN STORM 2. IV. Swift X-ray and ultraviolet/optical monitoring of Mrk 817

Authors: Edward M. Cackett, Jonathan Gelbord, Aaron J. Barth, Gisella De Rosa, Rick Edelson, Michael R. Goad, Yasaman Homayouni, Keith Horne, Erin A. Kara, Gerard A. Kriss, Kirk T. Korista, Hermine Landt, Rachel Plesha, Nahum Arav, Misty C. Bentz, Benjamin D. Boizelle, Elena Dalla Bonta, Maryam Dehghanian, Fergus Donnan, Pu Du, Gary J. Ferland, Carina Fian, Alexei V. Filippenko, Diego H. Gonzalez Buitrago, Catherine J. Grier , et al. (26 additional authors not shown)

Abstract: The AGN STORM 2 campaign is a large, multiwavelength reverberation mapping project designed to trace out the structure of Mrk 817 from the inner accretion disk to the broad emission line region and out to the dusty torus. As part of this campaign, Swift performed daily monitoring of Mrk 817 for approximately 15 months, obtaining observations in X-rays and six UV/optical filters. The X-ray monitori… ▽ More The AGN STORM 2 campaign is a large, multiwavelength reverberation mapping project designed to trace out the structure of Mrk 817 from the inner accretion disk to the broad emission line region and out to the dusty torus. As part of this campaign, Swift performed daily monitoring of Mrk 817 for approximately 15 months, obtaining observations in X-rays and six UV/optical filters. The X-ray monitoring shows that Mrk 817 was in a significantly fainter state than in previous observations, with only a brief flare where it reached prior flux levels. The X-ray spectrum is heavily obscured. The UV/optical light curves show significant variability throughout the campaign and are well correlated with one another, but uncorrelated with the X-rays. Combining the Swift UV/optical light curves with Hubble UV continuum light curves, we measure interband continuum lags, $τ(λ)$, that increase with increasing wavelength roughly following $τ(λ) \propto λ^{4/3}$, the dependence expected for a geometrically thin, optically thick, centrally illuminated disk. Modeling of the light curves reveals a period at the beginning of the campaign where the response of the continuum is suppressed compared to later in the light curve - the light curves are not simple shifted and scaled versions of each other. The interval of suppressed response corresponds to a period of high UV line and X-ray absorption, and reduced emission line variability amplitudes. We suggest that this indicates a significant contribution to the continuum from the broad line region gas that sees an absorbed ionizing continuum. △ Less

Submitted 26 September, 2023; v1 submitted 30 June, 2023; originally announced June 2023.

Comments: 20 pages, 13 figures, 3 tables, accepted for publication in ApJ

Ladder determinantal varieties and their symbolic blowups

Authors: Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt, Lisa Seccia, Matteo Varbaro

Abstract: In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal is strongly $F$-regular. Furthermore, we prove that the symbolic associated graded algebra of a mixed ladder determinantal ideal is $F$-pure. The latter implies that mixed ladder determinantal rings are $F$-pure. We also show that ideals of the poset of minors of a generic matrix give rise to $F$-pure alge… ▽ More In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal is strongly $F$-regular. Furthermore, we prove that the symbolic associated graded algebra of a mixed ladder determinantal ideal is $F$-pure. The latter implies that mixed ladder determinantal rings are $F$-pure. We also show that ideals of the poset of minors of a generic matrix give rise to $F$-pure algebras with straightening law. △ Less

Submitted 13 January, 2026; v1 submitted 29 May, 2023; originally announced May 2023.

Comments: Minor changes from v1

The core of monomial ideals

Authors: Louiza Fouli, Jonathan Montaño, Claudia Polini, Bernd Ulrich

Abstract: The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal $I$ satisfying certain residual conditions, showing that ${\rm core}(I)$ coincides with the largest monomial ideal contained in a general reduction of $I$. We prove that the class of lex-segment ideals satisfies these residual conditions an… ▽ More The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal $I$ satisfying certain residual conditions, showing that ${\rm core}(I)$ coincides with the largest monomial ideal contained in a general reduction of $I$. We prove that the class of lex-segment ideals satisfies these residual conditions and study the core of lex-segment ideals generated in one degree. For monomial ideals that do not necessarily satisfy the residual conditions and that are generated in one degree, we conjecture an explicit formula for the core, and make progress towards this conjecture. △ Less

Submitted 18 March, 2023; originally announced March 2023.

MSC Class: Primary: 13A30; 13B22; 05E40. Secondary: 14F18; 13C40; 13P10

AGN STORM 2: II. Ultraviolet Observations of Mrk817 with the Cosmic Origins Spectrograph on the Hubble Space Telescope

Authors: Y. Homayouni, Gisella De Rosa, Rachel Plesha, Gerard A. Kriss, Aaron J. Barth, Edward M. Cackett, Keith Horne, Erin A. Kara, Hermine Landt, Nahum Arav, Benjamin D. Boizelle, Misty C. Bentz, Thomas G. Brink, Michael S. Brotherton, Doron Chelouche, Elena Dalla Bonta, Maryam Dehghanian, Pu Du, Gary J. Ferland, Laura Ferrarese, Carina Fian, Alexei V. Filippenko, Travis Fischer, Ryan J. Foley, Jonathan Gelbord , et al. (40 additional authors not shown)

Abstract: We present reverberation mapping measurements for the prominent ultraviolet broad emission lines of the active galactic nucleus Mrk817 using 165 spectra obtained with the Cosmic Origins Spectrograph on the Hubble Space Telescope. Our ultraviolet observations are accompanied by X-ray, optical, and near-infrared observations as part of the AGN Space Telescope and Optical Reverberation Mapping Progra… ▽ More We present reverberation mapping measurements for the prominent ultraviolet broad emission lines of the active galactic nucleus Mrk817 using 165 spectra obtained with the Cosmic Origins Spectrograph on the Hubble Space Telescope. Our ultraviolet observations are accompanied by X-ray, optical, and near-infrared observations as part of the AGN Space Telescope and Optical Reverberation Mapping Program 2 (AGN STORM 2). Using the cross-correlation lag analysis method, we find significant correlated variations in the continuum and emission-line light curves. We measure rest-frame delayed responses between the far-ultraviolet continuum at 1180 A and Ly$α$ $\lambda1215$ A ($10.4_{-1.4}^{+1.6}$ days), N V $\lambda1240$ A ($15.5_{-4.8}^{+1.0}$days), SiIV + OIV] $\lambda1397$ A ($8.2_{-1.4}^{+1.4}$ days), CIV $\lambda1549$ A ($11.8_{-2.8}^{+3.0}$ days), and HeII $\lambda1640$ A ($9.0_{-1.9}^{+4.5}$ days) using segments of the emission-line profile that are unaffected by absorption and blending, which results in sampling different velocity ranges for each line. However, we find that the emission-line responses to continuum variations are more complex than a simple smoothed, shifted, and scaled version of the continuum light curve. We also measure velocity-resolved lags for the Ly$α$, and CIV emission lines. The lag profile in the blue wing of Ly$α$ is consistent with virial motion, with longer lags dominating at lower velocities, and shorter lags at higher velocities. The CIV lag profile shows the signature of a thick rotating disk, with the shortest lags in the wings, local peaks at $\pm$ 1500 $\rm km\,s^{-1}$, and a local minimum at line center. The other emission lines are dominated by broad absorption lines and blending with adjacent emission lines. These require detailed models, and will be presented in future work. △ Less

Submitted 22 February, 2023; originally announced February 2023.

Comments: Submitted to ApJ. 25 pages, 8 figures, and 6 tables

Generation of Large Vortex-Free Superfluid Helium Nanodroplets

Authors: Anatoli Ulmer, Andrea Heilrath, Björn Senfftleben, Sean M. O. O'Connell-Lopez, Björn Kruse, Lennart Seiffert, Katharina Kolatzki, Bruno Langbehn, Andreas Hoffmann, Thomas M. Baumann, Rebecca Boll, Adam S. Chatterley, Alberto De Fanis, Benjamin Erk, Swetha Erukala, Alexandra J. Feinberg, Thomas Fennel, Patrik Grychtol, Robert Hartmann, Markus Ilchen, Manuel Izquierdo, Bennet Krebs, Markus Kuster, Tommaso Mazza, Jacobo Montaño , et al. (16 additional authors not shown)

Abstract: Superfluid helium nanodroplets are an ideal environment for the formation of metastable, self-organized dopant nanostructures. However, the presence of vortices often hinders their formation. Here, we demonstrate the generation of vortex-free helium nanodroplets and explore the size range in which they can be produced. From x-ray diffraction images of xenon-doped droplets, we identify that single… ▽ More Superfluid helium nanodroplets are an ideal environment for the formation of metastable, self-organized dopant nanostructures. However, the presence of vortices often hinders their formation. Here, we demonstrate the generation of vortex-free helium nanodroplets and explore the size range in which they can be produced. From x-ray diffraction images of xenon-doped droplets, we identify that single compact structures, assigned to vortex-free aggregation, prevail up to $10^8$ atoms per droplet. This finding builds the basis for exploring the assembly of far-from-equilibrium nanostructures at low temperatures. △ Less

Submitted 20 June, 2023; v1 submitted 14 February, 2023; originally announced February 2023.

Comments: main article: 7 pages, 3 figures; supplementary material: 12 pages, 8 figures

UV/Optical disk reverberation lags despite a faint X-ray corona in the AGN Mrk 335

Authors: Erin Kara, Aaron J. Barth, Edward M. Cackett, Jonathan Gelbord, John Montano, Yan-Rong Li, Lisabeth Santana, Keith Horne, William N. Alston, Douglas Buisson, Doron Chelouche, Pu Du, Andrew C. Fabian, Carina Fian, Luigi Gallo, Michael R. Goad, Dirk Grupe, Diego H. Gonzalez Buitrago, Juan V. Hernandez Santisteban, Shai Kaspi, Chen Hu, S. Komossa, Gerard A. Kriss, Collin Lewin, Tiffany Lewis , et al. (15 additional authors not shown)

Abstract: We present the first results from a 100-day Swift, NICER and ground-based X-ray/UV/optical reverberation mapping campaign of the Narrow-Line Seyfert 1 Mrk 335, when it was in an unprecedented low X-ray flux state. Despite dramatic suppression of the X-ray variability, we still observe UV/optical lags as expected from disk reverberation. Moreover, the UV/optical lags are consistent with archival ob… ▽ More We present the first results from a 100-day Swift, NICER and ground-based X-ray/UV/optical reverberation mapping campaign of the Narrow-Line Seyfert 1 Mrk 335, when it was in an unprecedented low X-ray flux state. Despite dramatic suppression of the X-ray variability, we still observe UV/optical lags as expected from disk reverberation. Moreover, the UV/optical lags are consistent with archival observations when the X-ray luminosity was >10 times higher. Interestingly, both low- and high-flux states reveal UV/optical lags that are 6-11 times longer than expected from a thin disk. These long lags are often interpreted as due to contamination from the broad line region, however the u band excess lag (containing the Balmer jump from the diffuse continuum) is less prevalent than in other AGN. The Swift campaign showed a low X-ray-to-optical correlation (similar to previous campaigns), but NICER and ground-based monitoring continued for another two weeks, during which the optical rose to the highest level of the campaign, followed ~10 days later by a sharp rise in X-rays. While the low X-ray countrate and relatively large systematic uncertainties in the NICER background make this measurement challenging, if the optical does lead X-rays in this flare, this indicates a departure from the zeroth-order reprocessing picture. If the optical flare is due to an increase in mass accretion rate, this occurs on much shorter than the viscous timescale. Alternatively, the optical could be responding to an intrinsic rise in X-rays that is initially hidden from our line-of-sight. △ Less

Submitted 14 February, 2023; originally announced February 2023.

Comments: Accepted for publication in the Astrophysical Journal. 15 pages, 8 figures, 3 tables

K-polynomials of multiplicity-free varieties

Authors: Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi, Jonathan Montaño

Abstract: We describe the twisted $K$-polynomial of multiplicity-free varieties in a multiprojective setting. More precisely, for multiplicity-free varieties, we show that the support of the twisted $K$-polynomial is a generalized polymatroid. As applications, we show that the support of the Möbius function of a linear polymatroid is a generalized polymatroid, and we settle a conjecture of Monical, Tokcan a… ▽ More We describe the twisted $K$-polynomial of multiplicity-free varieties in a multiprojective setting. More precisely, for multiplicity-free varieties, we show that the support of the twisted $K$-polynomial is a generalized polymatroid. As applications, we show that the support of the Möbius function of a linear polymatroid is a generalized polymatroid, and we settle a conjecture of Monical, Tokcan and Yong regarding Grothendieck polynomials for the case of zero-one Schubert polynomials. △ Less

Submitted 12 June, 2025; v1 submitted 26 December, 2022; originally announced December 2022.

MSC Class: 14C17; 14M05; 14M15; 13H15; 52B40; 52B22

Purity of monoids and characteristic-free splittings in semigroup rings

Authors: Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt

Abstract: Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring associated to the monoid. Our results are characteristic independent. Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singularities and homological invariants of the semigroup ring associated to the monoid. Our results are characteristic independent. △ Less

Submitted 1 September, 2023; v1 submitted 7 October, 2022; originally announced October 2022.

Comments: to appear in Mathematische Zeitschrift

Optical Continuum Reverberation in the Dwarf Seyfert Nucleus of NGC 4395

Authors: John W. Montano, Hengxiao Guo, Aaron J. Barth, Vivian U, Raymond Remigio, Diego H. González-Buitrago, Juan V. Hernández Santisteban

Abstract: The nearby dwarf spiral galaxy NGC 4395 contains a broad-lined active galactic nucleus (AGN) of exceptionally low luminosity powered by accretion onto a central black hole of very low mass ($\sim10^4-10^5$ M$_\odot$). In order to constrain the size of the optical continuum emission region through reverberation mapping, we carried out high-cadence photometric monitoring of NGC 4395 in the $griz$ fi… ▽ More The nearby dwarf spiral galaxy NGC 4395 contains a broad-lined active galactic nucleus (AGN) of exceptionally low luminosity powered by accretion onto a central black hole of very low mass ($\sim10^4-10^5$ M$_\odot$). In order to constrain the size of the optical continuum emission region through reverberation mapping, we carried out high-cadence photometric monitoring of NGC 4395 in the $griz$ filter bands on two consecutive nights in 2022 April using the four-channel MuSCAT3 camera on the Faulkes Telescope North at Haleakalā Observatory. Correlated variability across the $griz$ bands is clearly detected, and the $r$, $i$, and $z$ band light curves show lags of $8.4^{+1.0}_{-1.1}$, $14.2^{+1.2}_{-1.4}$, and $20.4^{+2.0}_{-2.1}$ minutes with respect to the $g$ band when measured using the full-duration light curves. When lags are measured for each night separately, the Night 2 data exhibit lower cross-correlation amplitudes and shorter lags than the Night 1 light curves. Using the full-duration lags, we find that the lag-wavelength relationship is consistent with the $τ\proptoλ^{4/3}$ dependence found for more luminous AGN. Combining our results with continuum lags measured for other objects, the lag between $g$ and $z$ band scales with optical continuum luminosity as $τ_{gz} \propto L^{0.56\pm0.05}$, similar to the scaling of broad-line region size with luminosity, reinforcing recent evidence that diffuse continuum emission from the broad-line region may contribute substantially to optical continuum variability and reverberation lags. △ Less

Submitted 26 May, 2022; originally announced May 2022.

Comments: 8 pages, 3 figures, 2 tables, submitted to ApJL. Comments welcome

Frobenius methods in combinatorics

Authors: Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt

Abstract: We survey results produced from the interaction between methods in prime characteristic and combinatorial commutative algebra. We showcase results for edge ideals, toric varieties, Stanley-Reisner rings, and initial ideals that were proven via Frobenius. We also discuss results for monomial ideals obtained using Frobenius-like maps. Finally, we present results for $F$-pure rings that were inspired… ▽ More We survey results produced from the interaction between methods in prime characteristic and combinatorial commutative algebra. We showcase results for edge ideals, toric varieties, Stanley-Reisner rings, and initial ideals that were proven via Frobenius. We also discuss results for monomial ideals obtained using Frobenius-like maps. Finally, we present results for $F$-pure rings that were inspired by work done for Stanley-Reisner rings. △ Less

Submitted 18 March, 2022; originally announced March 2022.

Comments: 35 pages

Double Schubert polynomials do have saturated Newton polytopes

Authors: Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi, Jonathan Montaño

Abstract: We prove that double Schubert polynomials have the Saturated Newton Polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study non-standard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen-Macaulay prime… ▽ More We prove that double Schubert polynomials have the Saturated Newton Polytope property. This settles a conjecture by Monical, Tokcan and Yong. Our ideas are motivated by the theory of multidegrees. We introduce a notion of standardization of ideals that enables us to study non-standard multigradings. This allows us to show that the support of the multidegree polynomial of each Cohen-Macaulay prime ideal, and in particular, that of each Schubert determinantal ideal is a discrete polymatroid. △ Less

Submitted 9 October, 2023; v1 submitted 21 September, 2021; originally announced September 2021.

Comments: to appear in Forum of Mathematics, Sigma

MSC Class: 13H15; 14M15; 14C17; 52B40

Blowup algebras of determinantal ideals in prime characteristic

Authors: Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt

Abstract: We study when blowup algebras are $F$-split or strongly $F$-regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a symmetric matrix, and a Hankel matrix. We also study ideals of Pfaffians of a skew-symmetric matrix. We use these results to obtain bounds on the degrees of the defining equations for these algebras. We also prove that t… ▽ More We study when blowup algebras are $F$-split or strongly $F$-regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a symmetric matrix, and a Hankel matrix. We also study ideals of Pfaffians of a skew-symmetric matrix. We use these results to obtain bounds on the degrees of the defining equations for these algebras. We also prove that the limit of the normalized regularity of the symbolic powers of these ideals exists and that their depth stabilizes. Finally, we show that, for determinantal ideals, there exists a monomial order for which taking initial ideals commutes with taking symbolic powers. To obtain these results we develop the notion of $F$-split filtrations and symbolic $F$-split ideals. △ Less

Submitted 18 June, 2024; v1 submitted 1 September, 2021; originally announced September 2021.

Comments: Final version. This preprint corrects, replaces, and expands the work done in preprint arXiv:2004.03831, which contains a mistake Lemma 5.4. The new version changes some terminology. We also added a new result about F-regularity for symbolic Rees algebras of ideals associated to symmetric matrices (Theorem 6.16)

MSC Class: 13A30; 13A35; 13A02; 13C15

AGN STORM 2: I. First results: A Change in the Weather of Mrk 817

Authors: Erin Kara, Missagh Mehdipour, Gerard A. Kriss, Edward M. Cackett, Nahum Arav, Aaron J. Barth, Doyee Byun, Michael S. Brotherton, Gisella De Rosa, Jonathan Gelbord, Juan V. Hernandez Santisteban, Chen Hu, Jelle Kaastra, Hermine Landt, Yan-Rong Li, Jake A. Miller, John Montano, Ethan Partington, Jesus Aceituno, Jin-Ming Bai, Dongwei Bao, Misty C. Bentz, Thomas G. Brink, Doron Chelouche, Yong-Jie Chen , et al. (47 additional authors not shown)

Abstract: We present the first results from the ongoing, intensive, multi-wavelength monitoring program of the luminous Seyfert 1 galaxy Mrk 817. While this AGN was, in part, selected for its historically unobscured nature, we discovered that the X-ray spectrum is highly absorbed, and there are new blueshifted, broad and narrow UV absorption lines, which suggest that a dust-free, ionized obscurer located at… ▽ More We present the first results from the ongoing, intensive, multi-wavelength monitoring program of the luminous Seyfert 1 galaxy Mrk 817. While this AGN was, in part, selected for its historically unobscured nature, we discovered that the X-ray spectrum is highly absorbed, and there are new blueshifted, broad and narrow UV absorption lines, which suggest that a dust-free, ionized obscurer located at the inner broad line region partially covers the central source. Despite the obscuration, we measure UV and optical continuum reverberation lags consistent with a centrally illuminated Shakura-Sunyaev thin accretion disk, and measure reverberation lags associated with the optical broad line region, as expected. However, in the first 55 days of the campaign, when the obscuration was becoming most extreme, we observe a de-coupling of the UV continuum and the UV broad emission line variability. The correlation recovers in the next 42 days of the campaign, as Mrk 817 enters a less obscured state. The short CIV and Ly alpha lags suggest that the accretion disk extends beyond the UV broad line region. △ Less

Submitted 12 May, 2021; originally announced May 2021.

Comments: 28 pages, 14 figures, submitted to ApJ. Comments welcome

Computing multiplicity sequences

Authors: Justin Chen, Youngsu Kim, Jonathan Montaño

Abstract: The MultiplicitySequence package for Macaulay2 computes the multiplicity sequence of a graded ideal in a standard graded ring over a field, as well as several invariants of monomial ideals related to integral dependence. We discuss two strategies implemented for computing multiplicity sequences: one via the bivariate Hilbert polynomial, and the other via the technique of general elements. The MultiplicitySequence package for Macaulay2 computes the multiplicity sequence of a graded ideal in a standard graded ring over a field, as well as several invariants of monomial ideals related to integral dependence. We discuss two strategies implemented for computing multiplicity sequences: one via the bivariate Hilbert polynomial, and the other via the technique of general elements. △ Less

Submitted 1 November, 2023; v1 submitted 25 March, 2021; originally announced March 2021.

Comments: 6 pages

MSC Class: 13H15; 13-04

Journal ref: J. Softw. Alg. Geom. 14 (2024) 13-18

The 1-Megapixel pnCCD Detector for the Small Quantum Systems Instrument at the European XFEL: System and Operation Aspects

Authors: Markus Kuster, Karim Ahmed, Kai-Erik Ballak, Cyril Danilevski, Marko Ekmedžić, Bruno Fernandes, Patrick Gessler, Robert Hartmann, Steffen Hauf, Peter Holl, Michael Meyer, Jacobo Montaño, Astrid Münnich, Yevheniy Ovcharenko, Nils Rennhack, Tonn Rüter, Daniela Rupp, Dieter Schlosser, Kiana Setoodehnia, Rüdiger Schmitt, Lothar Strüder, Rico Mayro P. Tanyag, Anatoli Ulmer, Hazem Yousef

Abstract: The X-ray free-electron lasers that became available during the last decade, like the European XFEL (EuXFEL), place high demands on their instrumentation. Especially at low photon energies below $1\,\text{keV}$, detectors with high sensitivity, and consequently low noise and high quantum efficiency, are required to enable facility users to fully exploit the scientific potential of the photon sourc… ▽ More The X-ray free-electron lasers that became available during the last decade, like the European XFEL (EuXFEL), place high demands on their instrumentation. Especially at low photon energies below $1\,\text{keV}$, detectors with high sensitivity, and consequently low noise and high quantum efficiency, are required to enable facility users to fully exploit the scientific potential of the photon source. A 1-Megapixel pnCCD detector with a $1024\times 1024$ pixel format has been installed and commissioned for imaging applications at the Nano-Sized Quantum System (NQS) station of the Small Quantum System (SQS) instrument at EuXFEL. The instrument is currently operating in the energy range between $0.5$ and $3\,\text{keV}$ and the NQS station is designed for investigations of the interaction of intense FEL pulses with clusters, nano-particles and small bio-molecules, by combining photo-ion and photo-electron spectroscopy with coherent diffraction imaging techniques. The core of the imaging detector is a pn-type charge coupled device (pnCCD) with a pixel pitch of $75\,μ\text{m}\times 75\,μ\text{m}$. Depending on the experimental scenario, the pnCCD enables imaging of single photons thanks to its very low electronic noise of $3$e$^-$ and high quantum efficiency. Here we present an overview on the EuXFEL pnCCD detector and the results from the commissioning and first user operation at the SQS experiment in June 2019. The detailed descriptions of the detector design and capabilities, its implementation at EuXFEL both mechanically and from the controls side as well as important data correction steps aim to provide useful background for users planning and analyzing experiments at EuXFEL and may serve as a benchmark for comparing and planning future endstations at other FELs. △ Less

Submitted 23 November, 2020; originally announced November 2020.

Comments: 10 pages, 10 figures, submitted to the Journal of Synchrotron Radiation

Mixed multiplicities of graded families of ideals

Authors: Yairon Cid-Ruiz, Jonathan Montaño

Abstract: We show the existence (and define) the mixed multiplicities of arbitrary graded families of ideals under mild assumptions. In particular, our methods and results are valid for the case of arbitrary $\mathfrak{m}$-primary graded families. Furthermore, we provide a far-reaching "Volume = Multiplicity formula" for the mixed multiplicities of graded families of ideals. We show the existence (and define) the mixed multiplicities of arbitrary graded families of ideals under mild assumptions. In particular, our methods and results are valid for the case of arbitrary $\mathfrak{m}$-primary graded families. Furthermore, we provide a far-reaching "Volume = Multiplicity formula" for the mixed multiplicities of graded families of ideals. △ Less

Submitted 1 May, 2021; v1 submitted 22 October, 2020; originally announced October 2020.

Comments: 15 pages

Convex bodies and graded families of monomial ideals

Authors: Yairon Cid-Ruiz, Jonathan Montaño

Abstract: We show that the mixed volumes of arbitrary convex bodies are equal to mixed multiplicities of graded families of monomial ideals, and to normalized limits of mixed multiplicities of monomial ideals. This result evinces the close relation between the theories of mixed volumes from convex geometry and mixed multiplicities from commutative algebra. We show that the mixed volumes of arbitrary convex bodies are equal to mixed multiplicities of graded families of monomial ideals, and to normalized limits of mixed multiplicities of monomial ideals. This result evinces the close relation between the theories of mixed volumes from convex geometry and mixed multiplicities from commutative algebra. △ Less

Submitted 17 February, 2021; v1 submitted 15 October, 2020; originally announced October 2020.

MSC Class: Primary 52A39; 13H15; Secondary 05E40; 11H06

Revisiting the rare $H\to q_iq_j$ decays in the Standard Model

Authors: J. I. Aranda, G. González-Estrada, J. Montaño, F. Ramírez-Zavaleta, E. S. Tututi

Abstract: We revisit the rare decays of the Higgs boson to two different quarks in the Standard Model, which arise at the one-loop level. We perform Taylor series expansions to the complete form factors of the decay amplitudes, according to their different mass hierarchies, this allow us to take full advantage of the GIM mechanism to eliminate spurious contributions and retain those that truly contribute. W… ▽ More We revisit the rare decays of the Higgs boson to two different quarks in the Standard Model, which arise at the one-loop level. We perform Taylor series expansions to the complete form factors of the decay amplitudes, according to their different mass hierarchies, this allow us to take full advantage of the GIM mechanism to eliminate spurious contributions and retain those that truly contribute. We found that Br$(H\to uc)$=$5.00\times10^{-20}$, Br$(H\to ds)$=$1.19\times10^{-11}$, Br$(H\to db)$=$5.16\times10^{-9}$ and Br$(H\to sb)$=$1.15\times10^{-7}$. Our predictions for the $H\to uc,ds$ decays disagree with previous results in the literature. △ Less

Submitted 15 September, 2020; originally announced September 2020.

Comments: 11 pages, 1 figure. Accepted manuscript version

Revisiting the top quark chromomagnetic dipole moment in the SM

Authors: J. I. Aranda, T. Cisneros-Pérez, J. Montaño, B. Quezadas-Vivian, F. Ramírez-Zavaleta, E. S. Tututi

Abstract: We revisit the anomalous chromomagnetic dipole moment in the Standard Model and show that its triple gluon vertex contribution, with the on-shell gluon ($q^2=0$), generates an infrared divergent pole. Consequently, the chromomagnetic dipole should not be perturbatively evaluated at $q^2=0$. Focusing on this top quark anomaly, denoted as $\hatμ_t(q^2)$, we compute it with the off-shell gluon with a… ▽ More We revisit the anomalous chromomagnetic dipole moment in the Standard Model and show that its triple gluon vertex contribution, with the on-shell gluon ($q^2=0$), generates an infrared divergent pole. Consequently, the chromomagnetic dipole should not be perturbatively evaluated at $q^2=0$. Focusing on this top quark anomaly, denoted as $\hatμ_t(q^2)$, we compute it with the off-shell gluon with a large momentum transfer, just as the $α_s(m_Z^2)$ convention scale, for both spacelike $q^2=-m_Z^2$ and timelike $q^2=m_Z^2$ cases. We found that $\hatμ_t(-m_Z^2)$ $=$ $-0.0224$ $-0.000925i$ and $\hatμ_t(m_Z^2)$ $=$ $-0.0133$ $-0.0267i$. Our $\mathrm{Re}\thinspace\hatμ_t(-m_Z^2)$ matches well with the current experimental value $\hatμ_t^\mathrm{Exp}=-0.024_{-0.009}^{+0.013}(\mathrm{stat})_{-0.011}^{+0.016}(\mathrm{syst})$, and the $\mathrm{Im}\thinspace\hatμ_t(-m_Z^2)$ part is induced by flavour changing charged currents. △ Less

Submitted 23 January, 2021; v1 submitted 10 September, 2020; originally announced September 2020.

Comments: 20 pages, 4 figures, this version matches with the published one

Bounds on Lorentz-violating Yukawa couplings via lepton electromagnetic moments

Authors: J. Alfonso Ahuatzi-Avendaño, Javier Montaño, Héctor Novales-Sánchez, Mónica Salinas, J. Jesús Toscano

Abstract: The effective-Lagrangian description of Lorentz-invariance violation provided by the so-called Standard-Model Extension covers all the sectors of the Standard Model, allowing for model-independent studies of high-energy phenomena that might leave traces at relatively-low energies. In this context, the quantification of the large set of parameters characterizing Lorentz-violating effects is well mo… ▽ More The effective-Lagrangian description of Lorentz-invariance violation provided by the so-called Standard-Model Extension covers all the sectors of the Standard Model, allowing for model-independent studies of high-energy phenomena that might leave traces at relatively-low energies. In this context, the quantification of the large set of parameters characterizing Lorentz-violating effects is well motivated. In the present work, effects from the Lorentz-nonconserving Yukawa sector on the electromagnetic moments of charged leptons are calculated, estimated, and discussed. Following a perturbative approach, explicit expressions of leading contributions are derived and upper bounds on Lorentz violation are estimated from current data on electromagnetic moments. Scenarios regarding the coefficients of Lorentz violation are considered. In a scenario of two-point insertions preserving lepton flavor, the bound on the electron electric dipole moment yields limits as stringent as $10^{-28}$, whereas muon and tau-lepton electromagnetic moments determine bounds as restrictive as $10^{-14}$ and $10^{-6}$, respectively. Another scenario, defined by the assumption that Lorentz-violating Yukawa couplings are Hermitian, leads to less stringent bounds, provided by the muon anomalous magnetic moment, which turn out to be as restrictive as $10^{-14}$. △ Less

Submitted 27 August, 2020; originally announced August 2020.

Comments: 21 pages, 17 figures, 6 tables

Journal ref: Phys. Rev. D 103, 055003 (2021)

Radiative neutrino masses and exotic right-handed neutrinos

Authors: A. C. B. Machado, J. Montaño, V. Pleitez, M. C. Rodriguez

Abstract: We consider an extension of the standard electroweak model with three Higgs doublets and global $B-L$ and $\mathbb{Z}_2$ symmetries. Two of the scalar doublets are inert due to the $\mathbb{Z}_2$ symmetry. We calculated all the mass spectra in the scalar and lepton sectors and accommodate the leptonic mixing matrix as well. We also include an analysis of the scalar sector, showing that the potenti… ▽ More We consider an extension of the standard electroweak model with three Higgs doublets and global $B-L$ and $\mathbb{Z}_2$ symmetries. Two of the scalar doublets are inert due to the $\mathbb{Z}_2$ symmetry. We calculated all the mass spectra in the scalar and lepton sectors and accommodate the leptonic mixing matrix as well. We also include an analysis of the scalar sector, showing that the potential is limited from below, and we obtain the masses of the scalar sector. Furthermore we consider the effects of the model on the anaomalous magnetic dipole of charged leptons and the $μ\to eγ$ decay. We also present the SUSY version of the model with global $B-L$. △ Less

Submitted 6 October, 2020; v1 submitted 27 July, 2020; originally announced July 2020.

Comments: 18 pages, 7 figures, corrected typos. arXiv admin note: text overlap with arXiv:1705.01009

Exterior powers and Tor-persistence

Authors: Justin Lyle, Jonathan Montaño, Keri Sather-Wagstaff

Abstract: A commutative Noetherian ring $R$ is said to be Tor-persistent if, for any finitely generated $R$-module $M$, the vanishing of $\operatorname{Tor}_i^R(M,M)$ for $i\gg 0$ implies $M$ has finite projective dimension. An open question of Avramov, et. al. asks whether any such $R$ is Tor-persistent. In this work, we exploit properties of exterior powers of modules and complexes to provide several part… ▽ More A commutative Noetherian ring $R$ is said to be Tor-persistent if, for any finitely generated $R$-module $M$, the vanishing of $\operatorname{Tor}_i^R(M,M)$ for $i\gg 0$ implies $M$ has finite projective dimension. An open question of Avramov, et. al. asks whether any such $R$ is Tor-persistent. In this work, we exploit properties of exterior powers of modules and complexes to provide several partial answers to this question; in particular, we show that every local ring $(R,\mathfrak{m})$ with $\mathfrak{m}^3=0$ is Tor-persistent. As a consequence of our methods, we provide a new proof of the Tachikawa Conjecture for positively graded rings over a field of characteristic different from 2. △ Less

Submitted 26 July, 2024; v1 submitted 17 July, 2020; originally announced July 2020.

Improving Locality Sensitive Hashing by Efficiently Finding Projected Nearest Neighbors

Authors: Omid Jafari, Parth Nagarkar, Jonathan Montaño

Abstract: Similarity search in high-dimensional spaces is an important task for many multimedia applications. Due to the notorious curse of dimensionality, approximate nearest neighbor techniques are preferred over exact searching techniques since they can return good enough results at a much better speed. Locality Sensitive Hashing (LSH) is a very popular random hashing technique for finding approximate ne… ▽ More Similarity search in high-dimensional spaces is an important task for many multimedia applications. Due to the notorious curse of dimensionality, approximate nearest neighbor techniques are preferred over exact searching techniques since they can return good enough results at a much better speed. Locality Sensitive Hashing (LSH) is a very popular random hashing technique for finding approximate nearest neighbors. Existing state-of-the-art Locality Sensitive Hashing techniques that focus on improving performance of the overall process, mainly focus on minimizing the total number of IOs while sacrificing the overall processing time. The main time-consuming process in LSH techniques is the process of finding neighboring points in projected spaces. We present a novel index structure called radius-optimized Locality Sensitive Hashing (roLSH). With the help of sampling techniques and Neural Networks, we present two techniques to find neighboring points in projected spaces efficiently, without sacrificing the accuracy of the results. Our extensive experimental analysis on real datasets shows the performance benefit of roLSH over existing state-of-the-art LSH techniques. △ Less

Submitted 19 June, 2020; originally announced June 2020.

Comments: arXiv admin note: text overlap with arXiv:2003.06415

MSC Class: H.2.4 ACM Class: H.2.4

Journal ref: SISAP 2020. Lecture Notes in Computer Science, vol 12440. Springer, Cham

When are multidegrees positive?

Authors: Federico Castillo, Yairon Cid-Ruiz, Binglin Li, Jonathan Montaño, Naizhen Zhang

Abstract: Let $k$ be an arbitrary field, $P = P_k^{m_1} \times_k \cdots \times_k P_k^{m_p}$ be a multiprojective space over $k$, and $X \subseteq P$ be a closed subscheme of $P$. We provide necessary and sufficient conditions for the positivity of the multidegrees of $X$. As a consequence of our methods, we show that when $X$ is irreducible, the support of multidegrees forms a discrete algebraic polymatroid… ▽ More Let $k$ be an arbitrary field, $P = P_k^{m_1} \times_k \cdots \times_k P_k^{m_p}$ be a multiprojective space over $k$, and $X \subseteq P$ be a closed subscheme of $P$. We provide necessary and sufficient conditions for the positivity of the multidegrees of $X$. As a consequence of our methods, we show that when $X$ is irreducible, the support of multidegrees forms a discrete algebraic polymatroid. In algebraic terms, we characterize the positivity of the mixed multiplicities of a standard multigraded algebra over an Artinian local ring, and we apply this to the positivity of mixed multiplicities of ideals. Furthermore, we use our results to recover several results in the literature in the context of combinatorial algebraic geometry. △ Less

Submitted 10 August, 2020; v1 submitted 15 May, 2020; originally announced May 2020.

Comments: This is a generalized and expanded version of arXiv:1612.00154. Final version, to appear in Advances in Mathematics

Rare decays of the top quark mediated by Z' gauge bosons and flavor violation

Authors: J. I. Aranda, D. Espinosa-Gomez, J. Montano, F. Ramirez-Zavaleta, E. S. Tututi

Abstract: The rare top quark decays mediated by a new neutral massive gauge boson that is predicted in models with extended gauge symmetries are studied. We focus on the processes $t\to cV, uV$ induced at the one loop level, where $V =γ, g$, by considering different extended models. It is found that, within a broad range of mass of the new neutral gauge boson, the models predict branching ratios for the dec… ▽ More The rare top quark decays mediated by a new neutral massive gauge boson that is predicted in models with extended gauge symmetries are studied. We focus on the processes $t\to cV, uV$ induced at the one loop level, where $V =γ, g$, by considering different extended models. It is found that, within a broad range of mass of the new neutral gauge boson, the models predict branching ratios for the decays in study that are competitive with respect to the corresponding branching ratios in the standard model. In order to establish bound on our branching ratios, we consider the recent experimental bounds as $m_{Z^\prime}\geq$ 3.8-4.5 TeV, depending on the model, which also impose restrictions on our calculation. Even in this case, the resulting branching ratios are of the same order of magnitude as that predicted by the standard model. It should be noted that for the case of two models studied here, since no experimental bound exists to compare with, the results could be important, as they are, in the best of cases, two orders of magnitude larger than the predicted by the standard model. △ Less

Submitted 5 May, 2020; originally announced May 2020.

Comments: 8 pages and 5 figures

Symbolic powers of determinantal ideals in prime characteristic

Authors: Jonathan Montaño, Luis Núñez-Betancourt

Abstract: We study the symbolic powers of determinantal ideals of generic, generic symmetric, and Hankel matrices of variables, and of Pfaffians of generic skew-symmetric matrices, in prime characteristic. Specifically, we show that the limit $\lim\limits_{n\to\infty} \frac{\textrm{reg}(I^{(n)})}{n}$ exists and that $\textrm{depth}(R/I^{(n)})$ stabilizes for $n\gg 0$. Furthermore, we give explicit formulas… ▽ More We study the symbolic powers of determinantal ideals of generic, generic symmetric, and Hankel matrices of variables, and of Pfaffians of generic skew-symmetric matrices, in prime characteristic. Specifically, we show that the limit $\lim\limits_{n\to\infty} \frac{\textrm{reg}(I^{(n)})}{n}$ exists and that $\textrm{depth}(R/I^{(n)})$ stabilizes for $n\gg 0$. Furthermore, we give explicit formulas for the stable value of $\textrm{depth}(R/I^{(n)})$ in the generic and skew-symmetric cases. In order to show these results, we introduce the notion of symbolic $F$-purity of ideals which is satisfied by the classes of ideals mentioned above. Moreover, we find several properties satisfied by symbolic $F$-pure ideals. For example, we show that their symbolic Rees algebras and symbolic associated graded algebras are $F$-pure. As a consequence, their $a$-invariants and depths present good behaviors. In addition, we provide a Fedder's-like Criterion for symbolic $F$-purity. △ Less

Submitted 14 September, 2021; v1 submitted 8 April, 2020; originally announced April 2020.

Comments: This preprint contained an error in the proof of Lemma 5.4. The mistake has been corrected and the paper has been vastly expanded in another paper available at arXiv:2109.00592

mmLSH: A Practical and Efficient Technique for Processing Approximate Nearest Neighbor Queries on Multimedia Data

Authors: Omid Jafari, Parth Nagarkar, Jonathan Montaño

Abstract: Many large multimedia applications require efficient processing of nearest neighbor queries. Often, multimedia data are represented as a collection of important high-dimensional feature vectors. Existing Locality Sensitive Hashing (LSH) techniques require users to find top-k similar feature vectors for each of the feature vectors that represent the query object. This leads to wasted and redundant… ▽ More Many large multimedia applications require efficient processing of nearest neighbor queries. Often, multimedia data are represented as a collection of important high-dimensional feature vectors. Existing Locality Sensitive Hashing (LSH) techniques require users to find top-k similar feature vectors for each of the feature vectors that represent the query object. This leads to wasted and redundant work due to two main reasons: 1) not all feature vectors may contribute equally in finding the top-k similar multimedia objects, and 2) feature vectors are treated independently during query processing. Additionally, there is no theoretical guarantee on the returned multimedia results. In this work, we propose a practical and efficient indexing approach for finding top-k approximate nearest neighbors for multimedia data using LSH called mmLSH, which can provide theoretical guarantees on the returned multimedia results. Additionally, we present a buffer-conscious strategy to speed up the query processing. Experimental evaluation shows significant gains in performance time and accuracy for different real multimedia datasets when compared against state-of-the-art LSH techniques. △ Less

Submitted 22 June, 2020; v1 submitted 13 March, 2020; originally announced March 2020.

Comments: Submitted to SISAP 2020

MSC Class: H.2.4 ACM Class: H.2.4

Journal ref: SISAP 2020. Lecture Notes in Computer Science, vol 12440. Springer, Cham

Analytic spread and integral closure of integrally decomposable modules

Authors: Carles Bivià-Ausina, Jonathan Montaño

Abstract: We relate the analytic spread of a module expressed as the direct sum of two submodules with the analytic spread of its components. We also study a class of submodules whose integral closure can be obtained by means of a simple computer algebra procedure once the integral closure of each row ideal is known. In particular, we analyze a class of modules, not necessarily of maximal rank, whose integr… ▽ More We relate the analytic spread of a module expressed as the direct sum of two submodules with the analytic spread of its components. We also study a class of submodules whose integral closure can be obtained by means of a simple computer algebra procedure once the integral closure of each row ideal is known. In particular, we analyze a class of modules, not necessarily of maximal rank, whose integral closure is determined by the family of Newton polyhedra of their row ideals. △ Less

Submitted 29 September, 2020; v1 submitted 22 January, 2020; originally announced January 2020.

Comments: Final version, to appear in Nagoya Mathematical Journal

Efficient Bitmap-based Indexing and Retrieval of Similarity Search Image Queries

Authors: Omid Jafari, Parth Nagarkar, Jonathan Montaño

Abstract: Finding similar images is a necessary operation in many multimedia applications. Images are often represented and stored as a set of high-dimensional features, which are extracted using localized feature extraction algorithms. Locality Sensitive Hashing is one of the most popular approximate processing techniques for finding similar points in high-dimensional spaces. Locality Sensitive Hashing (LS… ▽ More Finding similar images is a necessary operation in many multimedia applications. Images are often represented and stored as a set of high-dimensional features, which are extracted using localized feature extraction algorithms. Locality Sensitive Hashing is one of the most popular approximate processing techniques for finding similar points in high-dimensional spaces. Locality Sensitive Hashing (LSH) and its variants are designed to find similar points, but they are not designed to find objects (such as images, which are made up of a collection of points) efficiently. In this paper, we propose an index structure, Bitmap-Image LSH (bImageLSH), for efficient processing of high-dimensional images. Using a real dataset, we experimentally show the performance benefit of our novel design while keeping the accuracy of the image results high. △ Less

Submitted 15 December, 2019; originally announced December 2019.

Comments: Submitted to 2020 IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI 2020)

MSC Class: H.2.4 ACM Class: H.2.4

Journal ref: 2020 IEEE Southwest Symposium on Image Analysis and Interpretation (SSIAI), Albuquerque, NM, USA, 2020, pp. 58-61