Miracle-dz/UniFAR-FTUs huggingface dataset:
Simulating symmetric time evolution with local operations

In closed systems, dynamical symmetries lead to conservation laws. However, conservation laws are not applicable to open systems that undergo irreversible transformations. More general selection rules are needed to determine whether, given two states, the transition from one state to the other is possible. The usual approach to the problem of finding such rules relies heavily on group theory and involves a detailed study of the structure of the respective symmetry group. We approach the problem in a completely new way by using entanglement to investigate the asymmetry properties of quantum states. To this end, we embed the space state of the system in a tensor product Hilbert space, whereby symmetric transformations between two states are replaced with local operations on their bipartite images. The embedding enables us to use the well-studied theory of entanglement to investigate the consequences of dynamic symmetries. Moreover, under reversible transformations, the entanglement of the bipartite image states becomes a conserved quantity. These entanglement-based conserved quantities are new and different from the conserved quantities based on expectation values of the Hamiltonian symmetry generators. Our method is not group-specific and applies to general symmetries associated with any compact semi-simple Lie group.
A sparse regular approximation lemma

We introduce a new variant of Szemer\'edi's regularity lemma which we call the "sparse regular approximation lemma" (SRAL). The input to this lemma is a graph $G$ of edge density $p$ and parameters $\epsilon, \delta$, where we think of $\delta$ as a constant. The goal is to construct an $\epsilon$-regular partition of $G$ while having the freedom to add/remove up to $\delta |E(G)|$ edges. As we show here, this weaker variant of the regularity lemma already suffices for proving the graph removal lemma and the hypergraph regularity lemma, which are two of the main applications of the (standard) regularity lemma. This of course raises the following question: can one obtain quantitative bounds for SRAL that are significantly better than those associated with the regularity lemma? Our first result answers the above question affirmatively by proving an upper bound for SRAL given by a tower of height $O(\log 1/p)$. This allows us to reprove Fox's upper bound for the graph removal lemma. Our second result is a matching lower bound for SRAL showing that a tower of height $\Omega(\log 1/p)$ is unavoidable. We in fact prove a more general multicolored lower bound which is essential for proving lower bounds for the hypergraph regularity lemma.
Harmonic Analysis and Random Schr\"odinger Operators

This survey is based on a series of lectures given during the School on Random Schrödinger Operators and the International Conference on Spectral Theory and Mathematical Physics at the Pontificia Universidad Catolica de Chile, held in Santiago in November 2014. As the title suggests, the presented material has two foci: Harmonic analysis, more precisely, unique continuation properties of several natural function classes and Schrödinger operators, more precisely properties of their eigenvalues, eigenfunctions and solutions of associated differential equations. It mixes topics from (rather) pure to (rather) applied mathematics, as well as classical questions and results dating back a whole century to very recent and even unpublished ones. The selection of material covered is based on the selection made for the minicourse, and is certainly a personal choice corresponding to the research interests of the authors. Emphasis is layed not so much on proofs, but rather on concepts, questions, results, examples and applications. In several cases, however, we do supply proofs of special cases
On Lipschitz Continuous Optimal Stopping Boundaries

We obtain a probabilistic proof of the local Lipschitz continuity for the optimal stopping boundary of a class of problems with state space $[0,T]\times\mathbb{R}^d$, $d\ge 1$. To the best of our knowledge this is the only existing proof that relies exclusively upon stochastic calculus, all the other proofs making use of PDE techniques and integral equations. Thanks to our approach we obtain our result for a class of diffusions whose associated second order differential operator is not necessarily uniformly elliptic. The latter condition is normally assumed in the related PDE literature.
Health-Analytics Readiness Assessment: Elaborated Action Design Research and Nascent Theoretical Implications

Health analytics (HA) technology enables and enhances fact-based decision-making capabilities of hospitals in the clinical, operational, and administrative domains. It is, however, the case that HA success presupposes a hospital's readiness to adopt, absorb, and put the technology to effective use. Currently, there is a paucity of research that focuses on how hospital executives can assess their organization's readiness for HA. The principal objective of our study is to fill this gap. We design HA readiness-assessment artifacts guided by cross-sectional case studies to inform the design and the elaborated action design research approach that extends past artifacts through iterative collaboration with practitioners and industry experts. This article details the design process and artifacts and highlights implications for nascent theory and generalizable knowledge.
Mechanistic View on the Effects of SGLT2 Inhibitors on Lipid Metabolism in Diabetic Milieu

Chronic hyperglycemia induces pathophysiologic pathways with negative effects on the metabolism of most substrates as well as lipids and lipoproteins, and thereby induces dyslipidemia. Thus, the diabetic milieu is commonly accompanied by different levels of atherogenic dyslipidemia, which is per se a major risk factor for subsequent complications such as atherosclerosis, coronary heart disease, acute myocardial infarction, ischemic stroke, and nephropathy. Therefore, readjusting lipid metabolism in the diabetic milieu is a major goal for preventing dyslipidemia-induced complications. Sodium-glucose cotransporter-2 (SGLT2) inhibitors are a class of relatively newly introduced antidiabetes drugs (including empagliflozin, canagliflozin, dapagliflozin, etc.) with potent hypoglycemic effects and can reduce blood glucose by inducing glycosuria. However, recent evidence suggests that they could also provide extra-glycemic benefits in lipid metabolism. It seems that they can increase fat burning and lipolysis, normalizing the lipid metabolism and preventing or improving dyslipidemia. Nevertheless, the exact mechanisms involved in this process are not well-understood. In this review, we tried to explain how these drugs could regulate lipid homeostasis and we presented the possible involved cellular pathways supported by clinical evidence.
Exploring institutional logics to dynamic ambidexterity in health information system implementation in the public health sector of Ethiopia

Information system (IS) implementation can often lead to inherently contradictory issues, standardization, and evolve‐ability, which requires different, sets of information technology (IT) governance mechanisms. Recent research advocate ambidexterity mechanisms which consider the contradictory logic for long‐term success yet it has paid little attention to resource‐constrained settings which is a source of contradiction for the lack of technical and financial resource. Using an interpretative approach, based on institutional logic and dynamic ambidexterity concepts, this study revealed how centralized, systemic, and IT logics shaped IT governance mechanisms toward centralized and ad hoc‐based decentralized structures. Furthermore, the study depicted how the lack of a common vision for IS implementation impeded defining roles, identifying and collaborating with similar initiatives that led the implementation to uncontrolled evolve‐ability. Despite the absence of a common vision in resource‐constrained settings, the study identified the importance of resource‐chasing collaboration among heterogeneous actors to achieve standardization and evolve‐ability at a certain level though not sufficient. The study proposed an ambidextrous implementation framework by combining dynamic ambidexterity and institutional logic concepts to complement the resource‐chased collaboration with major HIS logics‐based collaboration through devising common vision, strategy, and mechanisms which allows sensing, seizing, and reconfiguring the emergent heterogeneous system implementation initiatives to achieve standardization and evolve‐ability simultaneously.
Algebraic geometry approach to the Bethe equation for Hofstadter-type models

We study the diagonalization problem of certain Hofstadter-type models through the algebraic Bethe ansatz equation by the algebraic geometry method. When the spectral variables lie on a rational curve, we obtain the complete and explicit solutions for models with a rational magnetic flux, and discuss the Bethe equation of their thermodynamic flux limit. The algebraic geometry properties of the Bethe equation on high genus algebraic curves are investigated in accordance with physical considerations of the Hofstadter model.
The Local Langlands Correspondence for Simple Supercuspidal Representations of GL_n(F)

Let F be a non-archimedean local field of characteristic zero with residual characteristic p. In this paper, we present a simple proof and construction of the local Langlands correspondence for simple supercuspidal representations of GL_n(F), when p does not divide n. As an application, we prove Jacquet's conjecture on the local converse problem for GL_n(F) in the case of simple supercuspidal representations, for arbitrary p.
Low Intensity Respiratory Muscle Training in COVID-19 Patients after Invasive Mechanical Ventilation: A Retrospective Case-Series Study

Worldwide, healthcare systems had to respond to an exponential increase in COVID-19 patients with a noteworthy increment in intensive care units (ICU) admissions and invasive mechanical ventilation (IMV). The aim was to determine low intensity respiratory muscle training (RMT) effects in COVID-19 patients upon medical discharge and after an ICU stay with IMV. A retrospective case-series study was performed. Forty COVID-19 patients were enrolled and divided into twenty participants who received IMV during ICU stay (IMV group) and 20 participants who did not receive IMV nor an ICU stay (non-IMV group). Maximal expiratory pressure (PEmax), maximal inspiratory pressure (PImax), COPD assessment test (CAT) and Medical Research Council (MRC) dyspnea scale were collected at baseline and after 12 weeks of low intensity RMT. A greater MRC dyspnea score and lower PImax were shown at baseline in the IMV group versus the non-IMV group (p < 0.01). RMT effects on the total sample improved all outcome measurements (p < 0.05; d = 0.38–0.98). Intragroup comparisons after RMT improved PImax, CAT and MRC scores in the IMV group (p = 0.001; d = 0.94–1.09), but not for PImax in the non-IMV group (p > 0.05). Between-groups comparison after RMT only showed MRC dyspnea improvements (p = 0.020; d = 0.74) in the IMV group versus non-IMV group. Furthermore, PImax decrease was only predicted by the IMV presence (R2 = 0.378). Low intensity RMT may improve respiratory muscle strength, health related quality of life and dyspnea in COVID-19 patients. Especially, low intensity RMT could improve dyspnea level and maybe PImax in COVID-19 patients who received IMV in ICU.
Stochastic Block Models and Reconstruction

The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computer science. In its simplest form, the planted partition model is a model for random graphs on $n$ nodes with two equal-sized clusters, with an between-class edge probability of $q$ and a within-class edge probability of $p$. Although most of the literature on this model has focused on the case of increasing degrees (ie.\ $pn, qn \to \infty$ as $n \to \infty$), the sparse case $p, q = O(1/n)$ is interesting both from a mathematical and an applied point of view. A striking conjecture of Decelle, Krzkala, Moore and Zdeborov\'a based on deep, non-rigorous ideas from statistical physics gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if $p = a/n$ and $q = b/n$, then Decelle et al.\ conjectured that it is possible to cluster in a way correlated with the true partition if $(a - b)^2 > 2(a + b)$, and impossible if $(a - b)^2 C (a + b)$ for some sufficiently large $C$. We prove half of their prediction, showing that it is indeed impossible to cluster if $(a - b)^2 2(a + b)$. Following Decelle et al, our work establishes a rigorous connection between the clustering problem, spin-glass models on the Bethe lattice and the so called reconstruction problem. This connection points to fascinating applications and open problems.
Lecture, Discussion, Group Work, Repeat: Using Aerial Photography and Machine Learning to Study the Use of Writing-Related Pedagogies in STEM Courses and Their Impact on Different Student Subgroups

: Although Writing Across the Curriculum (WAC) has long focused on incorporating writing and related literacy activities into STEM education, the extent to which these pedagogies are widely used in STEM teaching remains unclear, as does their impact on student course performance, especially for underrepresented and marginalized student groups. Using a sample of 18 STEM courses at a private liberal arts university, this study uses unique empirical methods to reconsider, for STEM disciplines, Russell’s (1990) claim that WAC has failed to make a “permanent impact” on higher education by a) using photography to document classroom activities in real time and b) using machine learning to categorize these images to determine which learning activities are used in STEM instruction and in what proportions. We find that (a) lecture continues to dominate in STEM education and that (b) some active learning pedagogies (discussion and group work) have ambivalent relationships to course performance (which differ according to student subgroups defined by gender, race, national origin, and other factors) while WAC pedagogies like reading and writing, although rare, are associated with improved student course performance. In light of these findings, we suggest implications for STEM pedagogy, best practices, and future research to prioritize equitably designed pedagogy in STEM. informal writing; (b) using innovative assignment types; and (c) project-based learning,
On the strong Lefschetz question for uniform powers of general linear forms in $k[x,y,z]$

Schenck and Seceleanu proved that if $R = k[x,y,z]$, where $k$ is an infinite field, and $I$ is an ideal generated by any collection of powers of linear forms, then multiplication by a general linear form $L$ induces a homomorphism of maximal rank from any component of $R/I$ to the next. That is, $R/I$ has the {\em weak Lefschetz property}. Considering the more general {\em strong Lefschetz question} of when $\times L^j$ has maximal rank for $j \geq 2$, we give the first systematic study of this problem. We assume that the linear forms are general and that the powers are all the same, i.e. that $I$ is generated by {\em uniform} powers of general linear forms. We prove that for any number of such generators, $\times L^2$ always has maximal rank. We then specialize to almost complete intersections, i.e. to four generators, and we show that for $j = 3,4,5$ the behavior depends on the uniform exponent and on $j$, in a way that we make precise. In particular, there is always at most one degree where $\times L^j$ fails maximal rank. Finally, we note that experimentally all higher powers of $L$ fail maximal rank in at least two degrees.
ONIOM2-DFT study of N2, O2 and NO interaction with Ce-MOR: Active sites and thermodynamics

A theoretical study was carried out for the adsorption of N2, O2, NO and NO+ with Cerium (Ce) modified mordenite (MOR). A two-layer ONIOM2 (two layer Integrated molecular Orbital + molecular Mechanics) methodology was employed, combining UFF (Universal Force Field) and DFT (Density Functional Theory) calculations for the low and high level, respectively. The formation of active Ce species based on the adsorption of CeO+ on the crystallographic positions T1, T2 and T4 in the H-MOR was studied. The geometrical, vibrational and thermodynamic results indicate that the Ce atom of CeO+ binds exothermically and spontaneously to two of the non-equivalent (Om) crystallographic oxygens of MOR (TnOm1Om2) according to: T1O1O4, T1O2O3, T2O4O7, T2O5O7 and T4O7O10 (T: Al or Si). The results of the interaction of N2, O2, NO and NO+ with Ce-MOR indicate that only exothermic and spontaneous adsorptions occur on the active sites located over the main channel of the 12-membered ring (12-MR) according to T1O1O4, T2O5O7 and T4O7O10. In general, the Ce-MOR system stabilizes electrophilic [CeO(NO+)] species, with possible activity deNOx reactions in the presence of nucleophilic reductants such as NH3; while for CeO(NO) species adsorbed on MOR a dynamic equilibrium between κ1NO, κ1ON, κ2NO adsorptions is reported which could be applicable for deNOx catalysis in the absence of reductants. On the basis of thermodynamic reaction functions, it is proposed that the most likely site for the location of active CeO+ is T2O5O7.
SPDE Limits of Many Server Queues

A many-server queueing system is considered in which customers with independent and identically distributed service times enter service in the order of arrival. The state of the system is represented by a process that describes the total number of customers in the system, as well as a measure-valued process that keeps track of the ages of customers in service, leading to a Markovian description of the dynamics. Under suitable assumptions, a functional central limit theorem is established for the sequence of (centered and scaled) state processes as the number of servers goes to infinity. The limit process describing the total number in system is shown to be an Ito diffusion with a constant diffusion coefficient that is insensitive to the service distribution. The limit of the sequence of (centered and scaled) age processes is shown to be a Hilbert space valued diffusion that can also be characterized as the unique solution of a stochastic partial differential equation that is coupled with the Ito diffusion. Furthermore, the limit processes are shown to be semimartingales and to possess a strong Markov property.
Security screening FDTD simulations of the human body and enclosures in polarimetric radar and comparison with measurements

Finite-difference time-domain simulations have been made of a security screening polarimetric radar over the band 18 GHz to 26 GHz, comparing the results with a proof-of-concept system operating over the same band. The proof-of-concept radar is presented together with its calibration and measurement set-up. Measurements indicate the cross-polarisation returns from a human subject are approximately 10 % to 25 % of the co-polarisation returns. A simulation model has been built using the openEMS software to simulate the body of a human, using realistic primitive shapes and electrical properties appropriate for these frequencies, indicating cross-polar returns are in the region of 15 % of the co-polar responses, with the duration of the reflections lasting around 2 ns. The comparisons between the measurements and simulations are good and provide a qualitative understanding of what happens when security screening radar radiation impinges on the human body. The simulation is extended to two simple enclosures, a cubic box and a short cylinder having dimensions of 300 mm and wall thicknesses of 5 mm, which could be made of wood, cardboard, paper or plastic. Results indicate the cross-polar reflection ranges from 3% to 75 % of the co-polar and bursts of reflections are commensurate with reflections from the front and back surfaces, these being separated in time by 2 ns.
There exist multilinear Bohnenblust-Hille constants $(C_{n})_{n=1}^{\infty}$ with $\displaystyle \lim_{n\rightarrow \infty}(C_{n+1}-C_{n}) =0.$

The $n$-linear Bohnenblust-Hille inequality asserts that there is a constant $C_{n}\in\lbrack1,\infty)$ such that the $\ell_{\frac{2n}{n+1}}$-norm of $(U(e_{i_{^{1}}},.,e_{i_{n}}))_{i_{1},. i_{n}=1}^{N}$is bounded above by $C_{n}$ times the supremum norm of $U,$ regardless of the $n$-linear form $U:\mathbb{C}^{N}\times. \times\mathbb{C}^{N}% \rightarrow\mathbb{C}$ and the positive integer $N$ (the same holds for real scalars). The power $2n/(n+1)$ is sharp but the values and asymptotic behavior of the optimal constants remain a mystery. The first estimates for these constants had exponential growth. Very recently, a new panorama emerged and the importance, for many applications, of the knowledge of the optimal constants (denoted by $(K_{n})_{n=1}^{\infty}$) was stressed. The title of this paper is part of our Fundamental Lemma, one of the novelties presented here. It brings surprising new (and precise) information on the optimal constants (for both real and complex scalars). For instance, [K_{n+1}-K_{n}<\frac{0.87}{n^{0.473}}] for infinitely many $n$'s. In the case of complex scalars we present a curious formula, where $\pi,e$ and the famous Euler--Mascheroni constant $\gamma$ appear together: [K_{n}<1+(\frac{4}{\sqrt{\pi}}(1-e^{\gamma/2-1/2}) {\sum\limits_{j=1}^{n-1}}j^{^{\log_{2}(e^{-\gamma/2+1/2}) -1}%})] for all $n\geq2$. Numerically, the above formula shows a surprising low growth, [K_{n}<1.41(n-1)^{0.305}-0.04] for every integer $n \geq2$. We also provide a brief discussion on the interplay between the Kahane-Salem-Zygmund and the Bohnenblust-Hille (polynomial and multilinear) inequalities.
Non-meager free sets and independent families

Our main result is that, given a collection $\mathcal{R}$ of meager relations on a Polish space $X$ such that $|\mathcal{R}|\leq\omega$, there exists a dense Baire subspace $F$ of $X$ (equivalently, a nowhere meager subset $F$ of $X$) such that $F$ is $R$-free for every $R\in\mathcal{R}$. This generalizes a recent result of Banakh and Zdomskyy. As an application, we show that there exists a non-meager independent family on $\omega$, and define the corresponding cardinal invariant. Furthermore, assuming Martin's Axiom for countable posets, our result can be strengthened by substituting "$|\mathcal{R}|\leq\omega$" with "$|\mathcal{R}|<\mathfrak{c}$" and "Baire" with "completely Baire".
On the concordance genus of topologically slice knots

The concordance genus of a knot K is the minimum Seifert genus of all knots smoothly concordant to K. Concordance genus is bounded below by the 4-ball genus and above by the Seifert genus. We give a lower bound for the concordance genus of K coming from the knot Floer complex of K. As an application, we prove that there are topologically slice knots with 4-ball genus equal to one and arbitrarily large concordance genus.
On the dimensions of attractors of random self-similar graph directed iterated function systems

In this paper we propose a new model of random graph directed fractals that extends the current well-known model of random graph directed iterated function systems, $V$-variable attractors, and fractal and Mandelbrot percolation. We study its dimensional properties for similarities with and without overlaps. In particular we show that for the two classes of $1$-variable and $\infty$-variable random graph directed attractors we introduce, the Hausdorff and upper box counting dimension coincide almost surely, irrespective of overlap. Under the additional assumption of the uniform strong separation condition we give an expression for the almost sure Hausdorff and Assouad dimension.