Miracle-dz/UniFAR-FTUs huggingface dataset:
Geometry-Preserving Numerical Methods for Physical Systems with Finite-Dimensional Lie Algebras

We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie group action and then generates the discrete solution of the Lie system on the manifold via a solution of the Lie system on the Lie group. One major result from the integration of a Lie system on a Lie group is that one is able to solve all associated Lie systems on manifolds at the same time, and that Lie systems on Lie groups can be described through first-order systems of linear homogeneous ordinary differential equations (ODEs) in normal form. This brings a lot of advantages, since solving a linear system of ODEs involves less numerical cost. Specifically, we use two families of numerical schemes on the Lie group, which are designed to preserve its geometrical structure: the first one is based on the Magnus expansion, whereas the second is based on Runge–Kutta–Munthe–Kaas (RKMK) methods. Moreover, since the aforementioned action relates the Lie group and the manifold where the Lie system evolves, the resulting integrator preserves any geometric structure of the latter. We compare both methods for Lie systems with geometric invariants, particularly a class on Lie systems on curved spaces. We also illustrate the superiority of our method for describing long-term behavior and for differential equations admitting solutions whose geometric features depends heavily on initial conditions. As already mentioned, our milestone is to show that the method we propose preserves all the geometric invariants very faithfully, in comparison with non-geometric numerical methods.
Well-posedness and long-time behavior of a bulk-surface coupled Cahn-Hilliard-diffusion system with singular potential for lipid raft formation

We study a bulk-surface coupled system that describes the processes of lipid-phase separation and lipid-cholesterol interaction on cell membranes, in which cholesterol exchange between cytosol and cell membrane is also incorporated. The PDE system consists of a surface Cahn-Hilliard equation for the relative concentration of saturated/unsaturated lipids and a surface diffusion-reaction equation for the cholesterol concentration on the membrane, together with a diffusion equation for the cytosolic cholesterol concentration in the bulk. The detailed coupling between bulk and surface evolutions is characterized by a mass exchange term $q$. For the system with a physically relevant singular potential, we first prove the existence, uniqueness and regularity of global weak solutions to the full bulk-surface coupled system under suitable assumptions on the initial data and the mass exchange term $q$. Next, we investigate the large cytosolic diffusion limit that gives a reduction of the full bulk-surface coupled system to a system of surface equations with non-local contributions. Afterwards, we study the long-time behavior of global solutions in two categories, i.e., the equilibrium and non-equilibrium models according to different choices of the mass exchange term $q$. For the full bulk-surface coupled system with a decreasing total free energy, we prove that every global weak solution converges to a single equilibrium as $t\to +\infty$. For the reduced surface system with a mass exchange term of reaction type, we establish the existence of a global attractor.
Delegated Time-Lock Puzzle

Time-Lock Puzzles (TLPs) are cryptographic protocols that enable a client to lock a message in such a way that a server can only unlock it after a specific time period. However, existing TLPs have certain limitations: (i) they assume that both the client and server always possess sufficient computational resources and (ii) they solely focus on the lower time bound for finding a solution, disregarding the upper bound that guarantees a regular server can find a solution within a certain time frame. Additionally, existing TLPs designed to handle multiple puzzles either (a) entail high verification costs or (b) lack generality, requiring identical time intervals between consecutive solutions. To address these limitations, this paper introduces, for the first time, the concept of a"Delegated Time-Lock Puzzle"and presents a protocol called"Efficient Delegated Time-Lock Puzzle"(ED-TLP) that realises this concept. ED-TLP allows the client and server to delegate their resource-demanding tasks to third-party helpers. It facilitates real-time verification of solution correctness and efficiently handles multiple puzzles with varying time intervals. ED-TLP ensures the delivery of solutions within predefined time limits by incorporating both an upper bound and a fair payment algorithm. We have implemented ED-TLP and conducted a comprehensive analysis of its overheads, demonstrating the efficiency of the construction.
Geometric tool kit for higher spin gravity (part II): An introduction to Lie algebroids and their enveloping algebras

These notes provide a self-contained introduction to Lie algebroids, Lie-Rinehart algebras and their universal envelopes. This review is motivated by the speculation that higher-spin gauge symmetries should admit a natural formulation as enveloping algebras of Lie algebroids since rigid higher-spin algebras are enveloping algebras of Lie algebras. Nevertheless, the material covered here may be of general interest to anyone interested in the description of gauge symmetries, connections and covariant derivatives, in terms of Lie algebroids. In order to be self-contained, a concise introduction to the algebraic characterisation of vector bundles as projective modules over the algebra of functions on the base manifold is provided.
Bounds for Hecke eigenforms and their allied L-functions

We consider Hecke eigenforms and their allied L-functions from three aspects in this thesis. First we generalize the Iwaniec’s spectral large sieve estimates of Maass cusp form to the local version for all congruence groups Γ0(q). Our approach is based on an inequality [[33], Proposition] for a general bilinear form involving Kloosterman sums and Bessel functions. The exceptional eigenvalues emerge in the course of the proof. In the second part, we extend Luo’s result [29] to prove a general optimal bound for L−norms of the dihedral Maass forms associated to Hecke’s grossencharacters of a fixed real quadratic field. Given a fixed quadratic field K = Q( √ D) with discriminant D, we remove the condition that the narrow class number of K is 1. The key ingredients are Watson [45] and Ichino [15]’s formula and the local spectral large sieve inequality established in the first part. Finally we obtain a long equation intended to establish an upper bound for the second moment of symmetric square L-functions. Petersson trace formula plays an important role and we study thoroughly an analogue of Estermann series using Hurwitz zeta function and establish its meromorphic extension and functional equation. This work provides a useful approach to the further study of L( 2 , sym(f)).
QUANT: A Minimalist Interval Method for Time Series Classification

We show that it is possible to achieve the same accuracy, on average, as the most accurate existing interval methods for time series classification on a standard set of benchmark datasets using a single type of feature (quantiles), fixed intervals, and an 'off the shelf' classifier. This distillation of interval-based approaches represents a fast and accurate method for time series classification, achieving state-of-the-art accuracy on the expanded set of 142 datasets in the UCR archive with a total compute time (training and inference) of less than 15 minutes using a single CPU core.
New Lipschitz estimates and long-time asymptotic behavior for porous medium and fast diffusion equations

We obtain new estimates for the solution of both the porous medium and the fast diffusion equations by studying the evolution of suitable Lipschitz norms. Our results include instantaneous regularization for all positive times, long-time decay rates of the norms which are sharp and independent of the initial support, and new convergence results to the Barenblatt profile. Moreover, we address nonlinear diffusion equations including quadratic or bounded potentials as well. In the slow diffusion case, our strategy requires exponents close enough to 1, while in the fast diffusion case, our results cover any exponent for which the problem is well-posed and mass-preserving in the whole space.
Sampling from the Gibbs measure of the continuous random energy model and the hardness threshold

The continuous random energy model (CREM) is a toy model of disordered systems introduced by Bovier and Kurkova in 2004 based on previous work by Derrida and Spohn in the 80s. In a recent paper by Addario-Berry and Maillard, they raised the following question: what is the threshold $\beta_G$, at which sampling approximately the Gibbs measure at any inverse temperature $\beta>\beta_G$ becomes algorithmically hard? Here, sampling approximately means that the Kullback--Leibler divergence from the output law of the algorithm to the Gibbs measure is of order $o(N)$ with probability approaching $1$, as $N\rightarrow\infty$, and algorithmically hard means that the running time, the numbers of vertices queries by the algorithms, is beyond of polynomial order. The present work shows that when the covariance function $A$ of the CREM is concave, for all $\beta>0$, a recursive sampling algorithm on a renormalized tree approximates the Gibbs measure with running time of order $O(N^{1+\varepsilon})$. For $A$ non-concave, the present work exhibits a threshold $\beta_G<\infty$ such that the following hardness transition occurs: a) For every $\beta\leq \beta_G$, the recursive sampling algorithm approximates the Gibbs measure with running time of order $O(N^{1+\varepsilon})$. b) For every $\beta>\beta_G$, a hardness result is established for a large class of algorithms. Namely, for any algorithm from this class that samples the Gibbs measure approximately, there exists $z>0$ such that the running time of this algorithm is at least $e^{zN}$ with probability approaching $1$. In other words, it is impossible to sample approximately in polynomial-time the Gibbs measure in this regime. Additionally, we provide a lower bound of the free energy of the CREM that could hold its own value.
Tunneling to Holographic Traversable Wormholes

We study nonperturbative effects of quantum gravity in a system consisting of a coupled pair of holographic CFTs. The AdS$_4$/CFT$_3$ system has three possible ground states: two copies of empty AdS, a pair of extremal AdS black holes, and an eternal AdS traversable wormhole. We give a recipe for calculating transition rates via gravitational instantons and test it by calculating the emission rate of radiation shells from a black hole. We calculate the nucleation rate of a traversable wormhole between a pair of AdS-RN black holes in the canonical and microcanonical ensembles. Our results give predictions of nonpertubative quantum gravity that can be tested in a holographic simulation.
Non-Markovian dynamics of open quantum systems via auxiliary particles with exact operator constraint

We introduce an auxiliary-particle field theory to treat the non-Markovian dynamics of driven-dissipative quantum systems of the Jaynes-Cummings type. It assigns an individual quantum field to each reservoir state and provides an analytic, faithful representation of the coupled system-bath dynamics. We apply the method to a driven-dissipative photon Bose-Einstein condensate (BEC) coupled to a reservoir of dye molecules with electronic and vibronic excitations. The complete phase diagram of this system exhibits a hidden, non-Hermitian phase transition separating temporally oscillating from biexponentially decaying photon density correlations within the BEC. On one hand, this provides a qualitative distinction of the thermal photon BEC from a laser. On the other hand, it shows that one may continuously tune from the BEC to the lasing phase by circumventing a critical point. This auxiliary-particle method is generally applicable to the dynamics of open, non-Markovian quantum systems.
Accelerated Benders Decomposition for Variable-Height Transport Packaging Optimisation

This paper tackles the problem of finding optimal variable-height transport packaging. The goal is to reduce the empty space left in a box when shipping goods to customers, thereby saving on filler and reducing waste. We cast this problem as a large-scale mixed integer problem (with over seven billion variables) and demonstrate various acceleration techniques to solve it efficiently in about three hours on a laptop. We present a KD-Tree algorithm to avoid exhaustive grid evaluation of the 3D-bin-packing, provide analytical transformations to accelerate the Benders decomposition, and an efficient implementation of the Benders sub problem for significant memory savings and a three order of magnitude runtime speedup.
Beta-trees: Multivariate histograms with confidence statements

Multivariate histograms are difficult to construct due to the curse of dimensionality. Motivated by $k$-d trees in computer science, we show how to construct an efficient data-adaptive partition of Euclidean space that possesses the following two properties: With high confidence the distribution from which the data are generated is close to uniform on each rectangle of the partition; and despite the data-dependent construction we can give guaranteed finite sample simultaneous confidence intervals for the probabilities (and hence for the average densities) of each rectangle in the partition. This partition will automatically adapt to the sizes of the regions where the distribution is close to uniform. The methodology produces confidence intervals whose widths depend only on the probability content of the rectangles and not on the dimensionality of the space, thus avoiding the curse of dimensionality. Moreover, the widths essentially match the optimal widths in the univariate setting. The simultaneous validity of the confidence intervals allows to use this construction, which we call {\sl Beta-trees}, for various data-analytic purposes. We illustrate this by using Beta-trees for visualizing data and for multivariate mode-hunting.
Decomposition Ascribed Synergistic Learning for Unified Image Restoration

Learning to restore multiple image degradations within a single model is quite beneficial for real-world applications. Nevertheless, existing works typically concentrate on regarding each degradation independently, while their relationship has been less exploited to ensure the synergistic learning. To this end, we revisit the diverse degradations through the lens of singular value decomposition, with the observation that the decomposed singular vectors and singular values naturally undertake the different types of degradation information, dividing various restoration tasks into two groups, \ie, singular vector dominated and singular value dominated. The above analysis renders a more unified perspective to ascribe the diverse degradations, compared to previous task-level independent learning. The dedicated optimization of degraded singular vectors and singular values inherently utilizes the potential relationship among diverse restoration tasks, attributing to the Decomposition Ascribed Synergistic Learning (DASL). Specifically, DASL comprises two effective operators, namely, Singular VEctor Operator (SVEO) and Singular VAlue Operator (SVAO), to favor the decomposed optimization, which can be lightly integrated into existing image restoration backbone. Moreover, the congruous decomposition loss has been devised for auxiliary. Extensive experiments on blended five image restoration tasks demonstrate the effectiveness of our method.
The Star Formation Across Cosmic Time (SFACT) Survey. II. The First Catalog from a New Narrowband Survey for Emission-line Objects

Star Formation Across Cosmic Time (SFACT) is a new narrowband (NB) survey designed to detect faint emission-line galaxies (ELGs) and QSOs over a broad range of redshifts. Here we present the first list of SFACT candidates from our pilot-study fields. Using the WIYN 3.5 m telescope, we are able to achieve good image quality with excellent depth and routinely detect ELGs to r = 25.0. The limiting line flux of the survey is ∼1.0 × 10−16 erg s−1 cm−2. SFACT targets three primary emission lines: Hα, [O iii] λ5007, and [O ii] λ3727. The corresponding redshift windows allow for the detection of objects at z ∼ 0–1. With a coverage of 1.50 deg2 in our three pilot-study fields, a total of 533 SFACT candidates have been detected (355 candidates deg−2). We detail the process by which these candidates are selected in an efficient and primarily automated manner, then tabulate accurate coordinates, broadband photometry, and NB fluxes for each source.
A Fast Monte Carlo algorithm for evaluating matrix functions with application in complex networks

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods, which only work with one entry at a time, resulting in a significantly better convergence rate than the original approach. To assess the applicability of our method, we compute the subgraph centrality and total communicability of several large networks. In all benchmarks analyzed so far, the performance of our method was significantly superior to the competition, being able to scale up to 64 CPU cores with remarkable efficiency.
Designing a Communication Bridge between Communities: Participatory Design for a Question-Answering AI Agent

How do we design an AI system that is intended to act as a communication bridge between two user communities with different mental models and vocabularies? Skillsync is an interactive environment that engages employers (companies) and training providers (colleges) in a sustained dialogue to help them achieve the goal of building a training proposal that successfully meets the needs of the employers and employees. We used a variation of participatory design to elicit requirements for developing AskJill, a question-answering agent that explains how Skillsync works and thus acts as a communication bridge between company and college users. Our study finds that participatory design was useful in guiding the requirements gathering and eliciting user questions for the development of AskJill. Our results also suggest that the two Skillsync user communities perceived glossary assistance as a key feature that AskJill needs to offer, and they would benefit from such a shared vocabulary.
INVESTIGATION OF NEWTONIAN AND NON-NEWTONIAN DROPLETS IN COLLISION WITH THE HEATED ULTRAPHOBIC SURFACE ON VARIOUS WEBER NUMBERS

Super hydrophobic surfaces due to water repelling property, have a considerable potential for the use in various modern technologies. In this paper, the collision between Newtonian and non-Newtonian droplets with a super-hydrophobic hot surface like graphite has been simulated. The contact angle is 140 and 160 degree. Simulation yielded proper result compared to the experimental results. It is found that the temperature effect on hydrophobic surfaces is negligible. Our results demonstrate that the dimensionless drop diameter increases with the Weber number. It is revealed that a Newtonian droplets shows different behavior compared to a non-Newtonian one especially at higher temperatures.
Agent Inspired Trading Using Recurrent Reinforcement Learning and LSTM Neural Networks

With the breakthrough of computational power and deep neural networks, many areas that we haven't explore with various techniques that was researched rigorously in past is feasible. In this paper, we will walk through possible concepts to achieve robo-like trading or advising. In order to accomplish similar level of performance and generality, like a human trader, our agents learn for themselves to create successful strategies that lead to the human-level long-term rewards. The learning model is implemented in Long Short Term Memory (LSTM) recurrent structures with Reinforcement Learning or Evolution Strategies acting as agents The robustness and feasibility of the system is verified on GBPUSD trading.
Enhancing Representation Learning for Periodic Time Series with Floss: A Frequency Domain Regularization Approach

Time series analysis is a fundamental task in various application domains, and deep learning approaches have demonstrated remarkable performance in this area. However, many real-world time series data exhibit significant periodic or quasi-periodic dynamics that are often not adequately captured by existing deep learning-based solutions. This results in an incomplete representation of the underlying dynamic behaviors of interest. To address this gap, we propose an unsupervised method called Floss that automatically regularizes learned representations in the frequency domain. The Floss method first automatically detects major periodicities from the time series. It then employs periodic shift and spectral density similarity measures to learn meaningful representations with periodic consistency. In addition, Floss can be easily incorporated into both supervised, semi-supervised, and unsupervised learning frameworks. We conduct extensive experiments on common time series classification, forecasting, and anomaly detection tasks to demonstrate the effectiveness of Floss. We incorporate Floss into several representative deep learning solutions to justify our design choices and demonstrate that it is capable of automatically discovering periodic dynamics and improving state-of-the-art deep learning models.
Optimal design of plane elastic membranes using the convexified F\"{o}ppl's model

This work puts forth a new optimal design formulation for planar elastic membranes. The goal is to minimize the membrane's compliance through choosing the material distribution described by a positive Radon measure. The deformation of the membrane itself is governed by the convexified F\"{o}ppl's model. The uniqueness of this model lies in the convexity of its variational formulation despite the inherent nonlinearity of the strain-displacement relation. It makes it possible to rewrite the optimization problem as a pair of mutually dual convex variational problems. In the primal problem a linear functional is maximized with respect to displacement functions while enforcing that point-wisely the strain lies in an unbounded closed convex set. The dual problem consists in finding equilibrated stresses that are to minimize a convex integral functional of linear growth defined on the space of Radon measures. The pair of problems is analysed: existence and regularity results are provided, together with the system of optimality criteria. To demonstrate the computational potential of the pair, a finite element scheme is developed around it. Upon reformulation to a conic-quadratic&semi-definite programming problem, the method is employed to produce numerical simulations for several load case scenarios.