Tootfinder

Total Loss Functions for Measuring the Accuracy of Nonnegative Cross-Sectional Predictions
Charles D. Coleman
https://arxiv.org/abs/2507.15136 https://

Total Loss Functions for Measuring the Accuracy of Nonnegative Cross-Sectional Predictions
The total loss function associated with a set of cross-sectional predictions, that is, estimates or forecasts, summarizes the set's overall accuracy. Its arguments are the individual cross-sectional units' loss functions. Under general assumptions, including impartiality, about the forms of the individual loss functions, and the specific assumptions that the total loss function is anonymous and monotonic, only the additive, multiplicative and L-type (with restrictions) total loss functions are …

Exact versus Approximate Representations of Boolean Functions in the De Morgan Basis
Arkadev Chattopadhyay, Yogesh Dahiya, Shachar Lovett
https://arxiv.org/abs/2507.13963

Exact versus Approximate Representations of Boolean Functions in the De Morgan Basis
A seminal result of Nisan and Szegedy (STOC, 1992) shows that for any total Boolean function, the degree of the real polynomial that computes the function, and the minimal degree of a real polynomial that point-wise approximates the function, are at most polynomially separated. Extending this result from degree to other complexity measures like sparsity of the polynomial representation, or total weight of the coefficients, remains poorly understood. In this work, we consider this problem in t…

Two-Person Cooperative Games with delta-Rationality
Fang-Fang Tang, Yongsheng Xu
https://arxiv.org/abs/2506.16465 https://arxiv.org/p…

Two-Person Cooperative Games with delta-Rationality
A player's payoff is modeled as consisting of two parts: a rational-value part and a distortion-value part. It is argued that the (total) payoff function should be used to explain and predict the behaviors of the players, while the rational value function should be used to conduct welfare analysis of the final outcome. We use the Nash demand game to illustrate our model.

Robin Green Function Estimates and a Model of Mammalian Lungs
Guy David, Stefano Decio, Max Engelstein, Marcel Filoche, Svitlana Mayboroda, Marco Michetti
https://arxiv.org/abs/2507.13168

Robin Green Function Estimates and a Model of Mammalian Lungs
The present paper establishes delicate properties of the Green function with Robin boundary conditions, in particular, elucidating the nature of the passage between the Dirichlet-like and Neumann-like behavior. This yields sharp quantifiable bounds on the corresponding harmonic measure and proves the phase transition in the behavior of the total flow earlier conjectured in physics literature in concert with the efficacy of mammalian lungs.

Inversions in parking functions
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, Gabe Udell
https://arxiv.org/abs/2508.11587 https://…

Inversions in parking functions
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval parking functions to give analogous results. We conclude by introducing a probabilistic approach through which we obtain formulas for the total number of inversions and several other statistics across all parking functions and other sets of words closed under r…

Availability-Aware VNF Placement and Request Routing in MEC-Enabled 5G Networks
Aqsa Sayeed, Samaresh Bera
https://arxiv.org/abs/2508.14435 https://arxiv.o…

Availability-Aware VNF Placement and Request Routing in MEC-Enabled 5G Networks
In this paper, we study the virtual network function (VNF) placement problem in mobile edge computing (MEC)-enabled 5G networks to meet the stringent reliability and latency requirements of uRLLC applications. We pose it as a constrained optimization problem, which is NP-hard, to maximize the total reward obtained by a network service provider by serving uRLLC service requests. We propose an approximated randomized rounding approach to solve the NP-hard optimization problem in polynomial time. …

Variable selection for minimum-variance portfolios
Guilherme V. Moura, Andr\'e P. Santos, Hudson S. Torrent
https://arxiv.org/abs/2508.14986 https://ar…

Variable selection for minimum-variance portfolios
Machine learning (ML) methods have been successfully employed in identifying variables that can predict the equity premium of individual stocks. In this paper, we investigate if ML can also be helpful in selecting variables relevant for optimal portfolio choice. To address this question, we parameterize minimum-variance portfolio weights as a function of a large pool of firm-level characteristics as well as their second-order and cross-product transformations, yielding a total of 4,610 predicto…

Stochasticity in Stellar Yields Reflected in Theoretical Dust Masses Estimates Across all Type II Supernova Progenitors
Archana Purushothaman, Arkaprabha Sarangi, S. K. Jeena
https://arxiv.org/abs/2508.12933

Stochasticity in Stellar Yields Reflected in Theoretical Dust Masses Estimates Across all Type II Supernova Progenitors
Core-collapse supernovae (CCSNe) are among the primary sources of dust in galaxies. In this study, we derive theoretical upper limits on dust masses as a function of supernova (SN) progenitors with initial masses between 9 and 120 Msun, based on previously established models of dust formation chemistry in CCSNe. We find that O-rich dust, particularly silicates, dominates the dust budget, with masses ranging from 0.02 to 0.9 Msun, and that the total mass of O-rich dust increases with progenitor …

Group Fair Matchings using Convex Cost Functions
Atasi Panda, Harsh Sharma, Anand Louis, Prajakta Nimbhorkar
https://arxiv.org/abs/2508.12549 https://arxiv…

Group Fair Matchings using Convex Cost Functions
We consider the problem of assigning items to platforms where each item has a utility associated with each of the platforms to which it can be assigned. Each platform has a soft constraint over the total number of items it serves, modeled via a convex cost function. Additionally, items are partitioned into groups, and each platform also incurs group-specific convex cost over the number of items from each group that can be assigned to the platform. These costs promote group fairness by penalizin…

Unrolling Nonconvex Graph Total Variation for Image Denoising
Songlin Wei, Gene Cheung, Fei Chen, Ivan Selesnick
https://arxiv.org/abs/2506.02381 https://

Unrolling Nonconvex Graph Total Variation for Image Denoising
Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an $\ell_2$-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable …

Minimal tori in $\mathbb{R}^4$
Marc Soret, Marina Ville
https://arxiv.org/abs/2507.12914 https://arxiv.org/pdf/2507.12914

Minimal tori in $\mathbb{R}^4$
We describe tools for the study of minimal surfaces in $\mathbb{R}^4$; some are classical (the Gauss maps) and some are newer (the link/braid/writhe at infinity). Then we look for complete proper non holomorphic minimal tori with total curvature $-8π$ and a single end immersed in $\mathbb{R}^4$. We translate the problem into a system of $10$ quadratic or linear equations in $11$ real variables with coefficients in terms of the Weierstrass function $\wp$ and give explicit solutions for these eq…

Measurement of the Born cross section for $e^ e^- \to p K^- K^- \bar{\Xi}^ $ at $\sqrt{s} =$ 3.5-4.9 GeV
BESIII Collaboration, et al.
https://arxiv.org/abs/2508.11276 https://…

Measurement of the Born cross section for $e^+e^- \to p K^- K^- \barΞ^+$ at $\sqrt{s} =$ 3.5-4.9 GeV
Using $e^+ e^-$ collision data corresponding to a total integrated luminosity of 20 ${\rm fb}^{-1}$ collected with the BESIII detector at the BEPCII collider, we present a measurement of the Born cross section for the process $e^+e^- \to p K^-K^-\barΞ^{+}$ at 39 center-of-mass energies between 3.5 and 4.9 GeV with a partial reconstruction technique. By performing a fit to the dressed cross section of $e^{+}e^{-}\to p K^- K^-\barΞ^{+}$ with a power law function for continuum production and one…

A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization
Markus Friedemann, Gerd Wachsmuth
https://arxiv.org/abs/2508.10692 https:…

A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization
A solution algorithm for a special class of optimal control problems subject to an ordinary differential equation is proposed. The controls possess a continuous-or-off structure and are priced by a convex function. Additionally a total variation regularization is applied to penalize switches. Our solution method combines a trust-region method and a proximal gradient method. The subproblems are solved via Bellman's optimality principle. Convergence with respect to a criticality measure is proven…

Measurement of $\psi(2S)$ to $J/\psi$ cross-section ratio as function of multiplicity in $p$Pb collisions at$\sqrt{s_{NN}} = 8.16$ TeV
LHCb collaboration, et al.
https://arxiv.org/abs/2506.08624

Measurement of $ψ(2S)$ to $J/ψ$ cross-section ratio as function of multiplicity in $p$Pb collisions at$\sqrt{s_{NN}} = 8.16$ TeV
The production ratio of $ψ(2S)$ to $J/ψ$ charmonium states is presented as a function of multiplicity in proton-lead collisions at a centre-of-mass energy of $\sqrt{s_{NN}}=8.16$ TeV, for both prompt and nonprompt sources. The total luminosity recorded by the LHCb experiment corresponds to 13.6 $pb^{-1}$ for $p$Pb collisions and 20.8 $pb^{-1}$ for Pb$p$ collisions, where the first particle indicates the forward direction of the detector. Measurements are performed in the dimuon final state at…

Physical properties of galaxies and the UV Luminosity Function from $z\sim6$ to $z\sim14$ in COSMOS-Web
Maximilien Franco, Caitlin M. Casey, Hollis B. Akins, Olivier Ilbert, Marko Shuntov, Steven L. Finkelstein, Louise Paquereau, Andreas L. Faisst, Anton M. Koekemoer, Michaela Hirschmann, Sebastiano Cantarella, Nicole E. Drakos, Stephen M. Wilkins, Henry Joy McCracken, Jeyhan S. Kartaltepe, Claudia Maraston, Fatemeh Abedini, Mark J. Achenbach, Rafael C. Arango-Toro, Fabrizio Gentile, G…

Physical properties of galaxies and the UV Luminosity Function from $z\sim6$ to $z\sim14$ in COSMOS-Web
We present measurements of the rest-frame ultraviolet luminosity function (UVLF) in three redshift bins over $z\sim5.5$-14 from the JWST COSMOS-Web survey. Our samples, selected using the dropout technique in the HST/ACS F814W, JWST/NIRCam F115W, and F150W filters, contain a total of 3099 galaxies spanning a wide luminosity range from faint ($M_{\rm UV}\sim-19$ mag) to bright ($M_{\rm UV}\sim-22.5$ mag). The galaxies are undergoing rapid star formation, with blue stellar populations. Surprising…

Testing Coasting Cosmologies with Large-Scale Structure Growth
D\'avid A. K\"odm\"on, P\'eter Raffai
https://arxiv.org/abs/2506.11826 htt…

Testing Coasting Cosmologies with Large-Scale Structure Growth
We derive analytical expressions for the growth factor, $D(z)$, and density-weighted growth rate, $fσ_8(z)$, for coasting cosmologies, in which the scale factor is a linear function of time. We fit the latter to data from redshift space distortion measurements in the redshift range $z<2$ using the \texttt{dynesty} implementation of a nested sampling algorithm. In total, four models are tested: three coasting models with curvature parameters ${k=\{-1, 0, +1\}}$ in $H^2_0c^{-2}$ units, as well a…

Operator Decomposition via Total Sequences in Hilbert Spaces
Yunfan Zhao
https://arxiv.org/abs/2508.01978 https://arxiv.org/pdf/2508.01978

Operator Decomposition via Total Sequences in Hilbert Spaces
We investigate the structure of total sequences in complex Hilbert spaces and construct explicit representations of the identity operator as a series of rank-one operators. Given a total sequence ${v_n}_{n\in\mathbb{N}} \subseteq \mathcal{H}$, we establish the existence of sequences ${w_n}, {z_n} \subseteq \mathcal{H}$ and a monotonic function $φ: \mathbb{N} \to \mathbb{N}$ with $φ(n) \leq n$, such that $z_n$ lies in the span of ${v_k: k \geq φ(n)}$ and $\mathrm{id}{\mathcal{H}} = \sum_{n=1}…

This https://arxiv.org/abs/2502.10613 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Function recovery and optimal sampling in the presence of nonuniform evaluation costs
We consider recovering a function $f : D \rightarrow \mathbb{C}$ in an $n$-dimensional linear subspace $\mathcal{P}$ from i.i.d. pointwise samples via (weighted) least-squares estimators. Different from most works, we assume the cost of evaluating $f$ is potentially nonuniform, and governed by a cost function $c : D \rightarrow (0,\infty)$ which may blow up at certain points. We therefore strive to choose the sampling measure in a way that minimizes the expected total cost. We provide a recover…

Relaxed Total Generalized Variation Regularized Piecewise Smooth Mumford-Shah Model for Triangulated Surface Segmentation
Huayan Zhang, Shanqiang Wang, Xiaochao Wang
https://arxiv.org/abs/2507.19284

Relaxed Total Generalized Variation Regularized Piecewise Smooth Mumford-Shah Model for Triangulated Surface Segmentation
The Mumford-Shah (MS) model is an important technique for mesh segmentation. Many existing researches focus on piecewise constant MS mesh segmentation model with total variation regularization, which pursue the shortest length of boundaries. Different from previous efforts, in this article, we propose a novel piecewise smooth MS mesh segmentation model by utilizing the relaxed total generalized variation regularization (rTGV). The new model assumes that the feature function of a mesh can be app…

Wave-function microscopy: Derivation and anatomy of exact algebraic spinful wave functions and full Wigner-molecular spectra of a few highly correlated rapidly rotating ultracold fermionic atoms
Constantine Yannouleas, Uzi Landman
https://arxiv.org/abs/2506.08145

Wave-function microscopy: Derivation and anatomy of exact algebraic spinful wave functions and full Wigner-molecular spectra of a few highly correlated rapidly rotating ultracold fermionic atoms
Exploring strongly correlated spinful states of few fermionic ultracold atoms in a rapidly rotating trap, an example of which was recently realized for two fermionic $^6$Li atoms in an optical tweezer, we derive analytical (algebraic) total-spin-eigenstate wavefunctions through the development and employment of a theoretical platform that integrates exact numerical diagonalization (full configuration interaction, FCI) with symbolic language processing. For such rapid rotations, where the atoms …

A 2821 Star Optical SETI Survey using ESO HARPS archival data
Benjamin Fields, Jason C. Goodman
https://arxiv.org/abs/2508.08628 https://arxiv.org/pdf/2508…

A 2821 Star Optical SETI Survey using ESO HARPS archival data
We examined archived observations of 2,821 stars taken by the high-resolution ESO HARPS spectrograph to search for potential narrow-band laser emissions from extraterrestrial sources. From one observation of each star, our search algorithm identified a total of 285 spectral peaks with line widths slightly larger than the instrument's point-spread function. After eliminating false positives (including cosmic rays, instrumental artifacts, and terrestrial airglow lines, we identified 8 sources wor…

Dynamics of binding three independent ligands to a single scaffold
Eduardo D. Sontag
https://arxiv.org/abs/2508.06599 https://arxiv.org/pdf/2508.06599

Dynamics of binding three independent ligands to a single scaffold
This note considers a system in which three ligands can independently bind to a scaffold. Such systems arise in diverse applications, including immunotherapy and synthetic biology. It is shown that there are unique steady states in each conservation class, and these are asymptotically stable. The dependency of the steady-state amount of fully bound complex, as a function of total scaffold, is analyzed as well.

Density dependent embedding potentials for piecewise exact densities
Tomasz Adam Wesolowski
https://arxiv.org/abs/2506.08744 https://…

Density dependent embedding potentials for piecewise exact densities
Frozen Density Embedding Theory (FDET) [Wesolowski {\it Phys. Rev. A} {\bf 77}, 012504 (2008)] provides the interpretation of the eigenvalue equations for an embedded $N'$-electron wavefunction, in which the embedding operator is multiplicative, as the Euler-Lagrange equation corresponding to the constrained minimisation of the Hohenberg-Kohn energy functional. The constraint is given by a non-negative function integrating to an integer $N-N'>0$ with $N$ being the total number of electrons in t…

Bounded Weighted Edit Distance: Dynamic Algorithms and Matching Lower Bounds
Itai Boneh, Egor Gorbachev, Tomasz Kociumaka
https://arxiv.org/abs/2507.02548 …

Bounded Weighted Edit Distance: Dynamic Algorithms and Matching Lower Bounds
The edit distance $ed(X,Y)$ of two strings $X,Y\in Σ^*$ is the minimum number of character edits (insertions, deletions, and substitutions) needed to transform $X$ into $Y$. Its weighted counterpart $ed^w(X,Y)$ minimizes the total cost of edits, which are specified using a function $w$, normalized so that each edit costs at least one. The textbook dynamic-programming procedure, given strings $X,Y\in Σ^{\le n}$ and oracle access to $w$, computes $ed^w(X,Y)$ in $O(n^2)$ time. Nevertheless, one …

Flux of Extragalactic Dark Matter in Direct Detection Experiments
Shokhruz Kakharov, Abraham Loeb
https://arxiv.org/abs/2507.01190 https://

Flux of Extragalactic Dark Matter in Direct Detection Experiments
We calculate the contribution of extragalactic dark matter to the local dark matter density and flux in the Milky Way. By analyzing the Galactic escape velocity as a function of direction, we establish the criterion for separating dark matter particles bound to the Milky Way and those originating from the Local Group environment. Our analysis reveals that approximately 25% of dark matter particles in the Solar neighborhood have an extragalactic origin, contributing nearly 38% of the total mass …

A Finite-State Symbolic Automaton Model for the Collatz Map and Its Convergence Properties
Leonard Ben Aurel Brauer
https://arxiv.org/abs/2506.21728 https:…

A Finite-State Symbolic Automaton Model for the Collatz Map and Its Convergence Properties
We present a finite-state, deterministic automaton that emulates the Collatz function by operating on base-10 digit sequences. Each digit is represented as a symbolic triplet capturing its value, the parity of the next digit, and a local carry value, resulting in a state space of exactly 60 configurations. The transition rules are local, total, and parity-dependent, yet collectively reproduce the global behavior of the Collatz map through digitwise operations. All symbolic trajectories reduce t…

Downward self-reducibility in the total function polynomial hierarchy
Karthik Gajulapalli, Surendra Ghentiyala, Zeyong Li, Sidhant Saraogi
https://arxiv.org/abs/2507.19108 https…

Downward self-reducibility in the total function polynomial hierarchy
A problem $\mathcal{P}$ is considered downward self-reducible, if there exists an efficient algorithm for $\mathcal{P}$ that is allowed to make queries to only strictly smaller instances of $\mathcal{P}$. Downward self-reducibility has been well studied in the case of decision problems, and it is well known that any downward self-reducible problem must lie in $\mathsf{PSPACE}$. Harsha, Mitropolsky and Rosen [ITCS, 2023] initiated the study of downward self reductions in the case of search probl…

A linesearch-based derivative-free method for noisy black-box problems
Alberto De Santis, Giampaolo Liuzzi, Stefano Lucidi
https://arxiv.org/abs/2508.00495 https://

A linesearch-based derivative-free method for noisy black-box problems
In this work we consider unconstrained optimization problems. The objective function is known through a zeroth order stochastic oracle that gives an estimate of the true objective function. To solve these problems, we propose a derivative-free algorithm based on extrapolation techniques. Under reasonable assumptions we are able to prove convergence properties for the proposed algorithms. Furthermore, we also give a worst-case complexity result stating that the total number of iterations where t…

Role of non-extensivity $q$-parameter in tectonic seismic forecasting
Oscar Sotolongo-Costa, Miguel Eduardo Mora-Ramos
https://arxiv.org/abs/2508.04932 https://

Role of non-extensivity $q$-parameter in tectonic seismic forecasting
By writing total Tsallis entropy as a function of non-extensivity q-parameter withing the fragment-asperity model for earthquakes, a critical range of values is identified: 1.4

Perimeter on a manifold, with applications to partial differential equations
Satyanad Kichenassamy (DMA)
https://arxiv.org/abs/2507.04740 https://

Perimeter on a manifold, with applications to partial differential equations
The perimeter of a measurable subset of $\mathbb R^N$ is the total variation of its characteristic function. We generalize this notion to a subset $E$ of a closed Riemannian manifold. We show that the perimeter of $E$ is the limit of the hear kernel regularization of its characteristic function. A generalization of the isoperimetric inequality and of the Fleming-Rishel formula follow. These results are applied to a quasilinear elliptic problem in $\mathbb R^N$ for which the usual symmetrization…

Packing tetrahedrons in edge-weighted graphs
Wanting Sun, Shunan Wei, Donglei Yang
https://arxiv.org/abs/2506.07147 https://arxiv.org…

Packing tetrahedrons in edge-weighted graphs
We prove that for all $μ>0, t\in (0,1)$ and sufficiently large $n\in 4\mathbb{N}$, if $G$ is an edge-weighted complete graph on $n$ vertices with a weight function $w: E(G)\rightarrow [0,1]$ and the minimum weighted degree $δ^w(G)\geq (\tfrac{1+3t}{4}+μ)n$, then $G$ contains a $K_4$-factor where each copy of $K_4$ has total weight more than $6t$. This confirms a conjecture of Balogh--Kemkes--Lee--Young for the tetrahedron case.

Assembling and Modeling Stacked Disordered Metasurfaces
Miao Chen, Amit Sharma, Johann Michler, Xavier Maeder, Philippe Lalanne, Angelos Xomalis
https://arxiv.org/abs/2506.23666

Assembling and Modeling Stacked Disordered Metasurfaces
Disordered metasurfaces offer unique properties unattainable with periodic or ordered metasurfaces, notably the absence of deterministic interference effects at specific wavelengths and angles. In this work, we introduce a lithography-free nanofabrication approach to realize cascaded disordered plasmonic metasurfaces with sub-micron total thickness. We experimentally characterize their angle-resolved specular and diffuse reflections using the bidirectional reflection distribution function (BRDF…

This https://arxiv.org/abs/2506.04665 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

An O(log log n)-approximate budget feasible mechanism for subadditive valuations
In budget-feasible mechanism design, there is a set of items $U$, each owned by a distinct seller. The seller of item $e$ incurs a private cost $\overline{c}_e$ for supplying her item. A buyer wishes to procure a set of items from the sellers of maximum value, where the value of a set $S\subseteq U$ of items is given by a valuation function $v:2^U\to \mathbb{R}_+$. The buyer has a budget of $B \in \mathbb{R}_+$ for the total payments made to the sellers. We wish to design a mechanism that is tr…

Exciton Berryology
Henry Davenport, Johannes Knolle, Frank Schindler
https://arxiv.org/abs/2507.22983 https://arxiv.org/pdf/2507.22983

Exciton Berryology
In translationally invariant semiconductors that host exciton bound states, one can define an infinite number of possible exciton Berry connections. These correspond to the different ways in which a many-body exciton state, at fixed total momentum, can be decomposed into free electron and hole Bloch states that are entangled by an exciton envelope wave function. Inspired by the modern theory of polarization, we define an exciton projected position operator whose eigenvalues single out two uniqu…

On the motion of a point charge in a plate capacitor considering influence effects
Heinz-J\"urgen Schmidt, Thomas Br\"ocker
https://arxiv.org/abs/2506.06132

On the motion of a point charge in a plate capacitor considering influence effects
A point charge between the plates of a capacitor generates an influence charge distribution on the plates that modify the electric field acting upon the point charge. This effect is described by the well-known Dirichlet Green's function for the two parallel conducting plate problem for which we derive an infinite mirror charge series representation. At the line perpendicular to the plates and passing through the point charge this Green's function and hence the total force can be explicitly eval…

This https://arxiv.org/abs/2407.14441 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A normalized gradient flow method for computing ground states of spin-2 Bose-Einstein condensates
We propose and analyze an efficient and accurate numerical method for computing ground states of spin-2 Bose-Einstein condensates (BECs) by using the normalized gradient flow (NGF). In order to successfully extend the NGF to spin-2 BECs which has five components in the vector wave function but with only two physical constraints on total mass conservation and magnetization conservation, two important techniques are introduced for designing the proposed numerical method. The first one is to syste…

Bose-Hubbard model in the canonical ensemble: a beyond mean-field approach
Tista Banerjee
https://arxiv.org/abs/2508.01692 https://arxiv.org/pdf/2508.01692…

Bose-Hubbard model in the canonical ensemble: a beyond mean-field approach
Ultracold atoms in optical lattices are versatile testbeds to study and manipulate equilibrium and out-of-equilibrium aspects of quantum many-body systems whose behavior can be described by Hubbard-type Hamiltonians. In this paper, we consider an ansatz wave-function which respects total particle-number conservation for such systems and goes beyond mean-field theory; this wave-function has the same complexity in the number of parameters as the mean-field Gutzwiller ansatz, and captures quantum …

The HI-to-H2 transition in the Draco cloud
Nicola Schneider (I. Physik.Institut, University of Cologne), Volker Ossenkopf-Okada (I. Physik.Institut, University of Cologne), Markus Roellig (Physikalischer Verein, Frankfurt, I. Physik.Institut, University of Cologne), Daniel Seifried (I. Physik.Institut, University of Cologne), Ralf S. Klessen (University of Heidelberg, Zentrum fuer Astronomie, Heidelberg), Alexei G. Kritsuk (Physics Department, University of California, San Diego), Edua…

The HI-to-H2 transition in the Draco cloud
In recent decades, significant attention has been dedicated to analytical and observational studies of the atomic hydrogen (HI) to molecular hydrogen (H2) transition in the interstellar medium. We focussed on the Draco diffuse cloud to gain deeper insights into the physical properties of the transition from HI to H2. We employed the total hydrogen column density probability distribution function (N-PDF) derived from Herschel dust observations and the N(HI)-PDF obtained from HI data collected by…

On the domains of first order differential operators on the Sierpi\'{n}ski gasket
Waldemar Schefer
https://arxiv.org/abs/2506.08679 https://

On the domains of first order differential operators on the Sierpiński gasket
We study the first order structure of $L^2$-differential one-forms on the Sierpiński gasket. We consider piecewise energy finite functions related to one-forms, normal parts, and show self-similarity properties of one-forms as in the case of energy finite functions on the Sierpiński gasket. We introduce first order differential operators, taking functions into functions, that can be understood as total derivatives with respect to some reference function or form. The main result is a pointwise…

Neural Networks for Parameter Estimation of the Discretely Observed Hawkes Process
Jason J. Lambe, Feng Chen, Tom Stindl, Tsz-Kit Jeffrey Kwan
https://arxiv.org/abs/2506.01258

Neural Networks for Parameter Estimation of the Discretely Observed Hawkes Process
When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based inference in this setting, we propose to use a likelihood-free approach to parameter estimation, where a fully connected neural network (NN) is trained using simulated data to estimate the parameters of the Hawkes process from a summary statistic of the count data. A…

Millions of inequivalent quadratic APN functions in eight variables
Christof Beierle, Philippe Langevin, Gregor Leander, Alexandr Polujan, Shahram Rasoolzadeh
https://arxiv.org/abs/2508.04644

Millions of inequivalent quadratic APN functions in eight variables
The only known example of an almost perfect nonlinear (APN) permutation in even dimension was obtained by applying CCZ-equivalence to a specific quadratic APN function. Motivated by this result, there have been numerous recent attempts to construct new quadratic APN functions. Currently, 32,892 quadratic APN functions in dimension 8 are known and two recent conjectures address their possible total number. The first, proposed by Y. Yu and L. Perrin (Cryptogr. Commun. 14(6): 1359-1369, 2022), sug…

On the first Neumann eigenvalue for critical points of a weighted area functional with asymptotically flat ends
A. L. Mart\'inez-Trivi\~no
https://arxiv.org/abs/2507.20955 h…

On the first Neumann eigenvalue for critical points of a weighted area functional with asymptotically flat ends
In the following work, we obtain a lower bound for the first Neumann eingevalue of the drift Laplacian $Δ^φ$ for a family of properly embedded $[φ,\vec{e}_{3}]$-minimal surfaces in $\mathbb{R}^3$ with concave function $φ$ and asymptotically flat ends. As application, we obtain a control on the topology for that surfaces with finite total curvature. The strategy will consists in an integration of the Bouchner's formula by the works of A. Lichnerowicz and S. Brendle, R. Tsiamis and relate sai…

An O(log log n)-approximate budget feasible mechanism for subadditive valuations
Rian Neogi, Kanstantsin Pashkovich, Chaitanya Swamy
https://arxiv.org/abs/2506.04665

An O(log log n)-approximate budget feasible mechanism for subadditive valuations
In budget-feasible mechanism design, there is a set of items $U$, each owned by a distinct seller. The seller of item $e$ incurs a private cost $\overline{c}_e$ for supplying her item. A buyer wishes to procure a set of items from the sellers of maximum value, where the value of a set $S\subseteq U$ of items is given by a valuation function $v:2^U\to \mathbb{R}_+$. The buyer has a budget of $B \in \mathbb{R}_+$ for the total payments made to the sellers. We wish to design a mechanism that is tr…

Resonant Structures in $p{}^7\mathrm{Be}$ Scattering and Their Connection to the Astrophysical $S$-Factor
Anil Khachi
https://arxiv.org/abs/2506.20349 http…

Resonant Structures in $p{}^7\mathrm{Be}$ Scattering and Their Connection to the Astrophysical $S$-Factor
In this paper, we employ the Variable Phase Approach (VPA) to obtain the scattering phase shifts \( δ(E, r) \), amplitude function \( A(r) \), and radial wavefunction \( u(r) \) for various channels involved in the astrophysical reaction \( {}^7\mathrm{Be}(p,γ)^8\mathrm{B} \). Using the extracted phase shifts, we compute the total and partial cross sections. It is observed that the peaks in the partial cross section correspond to resonant states in the compound nucleus, which also manifest as…

The z = 9.625 Cosmic Gems Galaxy was a "Compact Blue Monster" Propelled by Massive Star Clusters
E. Vanzella, M. Messa, A. Adamo, F. Loiacono, M. Oguri, K. Sharon, L. D. Bradley, P. Bergamini, M. Meneghetti, A. Claeyssens, B. Welch, M. Bradac, A. Zanella, A. Bolamperti, F. Calura, T. Y-Y. Hsiao, E. Zackrisson, M. Ricotti, L. Christensen, J. M. Diego, F. E. Bauer, X. Xu, S. Fujimoto, C. Grillo, M. Lombardi, P. Rosati, T. Resseguier, A. Zitrin, A. Bik, J. Richard, Abdurro'…

The z = 9.625 Cosmic Gems Galaxy was a "Compact Blue Monster" Propelled by Massive Star Clusters
The recent discovery of five massive stellar clusters at z=9.625 in the Cosmic Gems has raised the question about the formation mechanism of star clusters in the first half Gyr after the Big-Bang. We infer the total stellar mass in clusters by normalizing and integrating the stellar cluster mass function (SCMF, dn(M)/dM ~ (n$_0$) $M^β$), assuming three different slopes $β$ = -1.5, -2.0 and -2.5 and different lower-mass limits between $10^2$ and $10^5$ Msun. The total integrated cluster stella…

On the entropy of the massive conformal gravity universe
F. F. Faria
https://arxiv.org/abs/2505.17171 https://arxiv.org/pdf/2505.1717…

On the entropy of the massive conformal gravity universe
We find that the total entropy of the massive conformal gravity universe is an increasing function of time, and therefore the cosmological model of the theory passes the generalized second law of thermodynamics test.

Interpolation-Based Gradient-Error Bounds for Use in Derivative-Free Optimization of Noisy Functions
Alejandro G. Marchetti, Dominique Bonvin
https://arxiv.org/abs/2507.19661 ht…

Interpolation-Based Gradient-Error Bounds for Use in Derivative-Free Optimization of Noisy Functions
In this paper, we analyze the accuracy of gradient estimates obtained by linear interpolation when the underlying function is subject to bounded measurement noise. The total gradient error is decomposed into a deterministic component arising from the interpolation (finite-difference) approximation, and a stochastic component due to noise. Various upper bounds for both error components are derived and compared through several illustrative examples. Our comparative study reveals that strict deter…

Three-boson scattering hypervolume for a nonzero orbital angular momentum
Pui In Ip, Shina Tan
https://arxiv.org/abs/2507.20787 https://arxiv.org/pdf/2507.…

Three-boson scattering hypervolume for a nonzero orbital angular momentum
We analyze the zero energy collision of three identical bosons in the same internal state with total orbital angular momentum $L=2$, assuming short range interactions. By solving the Schrödinger equation asymptotically, we derive two expansions of the wave function when three bosons are far apart or a pair of bosons and the third boson are far apart. The scattering hypervolume $D$ is defined for this collision. Unlike the scattering hypervolume defined by one of us in 2008, whose dimension is …