Large Language Models (LLMs) have shown impressive performance on various benchmarks, yet their ability to engage in deliberate reasoning remains questionable. We present NYT-Connections, a collection of 358 simple word classification puzzles derived from the New York Times Connections game. This benchmark is designed to penalize quick, intuitive "System 1" thinking, isolating fundamental reasoning skills. We evaluated six recent LLMs, a simple machine learning heuristic, and humans across three configurations: single-attempt, multiple attempts without hints, and multiple attempts with contextual hints. Our findings reveal a significant performance gap: even top-performing LLMs like GPT-4 fall short of human performance by nearly 30%. Notably, advanced prompting techniques such as Chain-of-Thought and Self-Consistency show diminishing returns as task difficulty increases. NYT-Connections uniquely combines linguistic isolation, resistance to intuitive shortcuts, and regular updates to mitigate data leakage, offering a novel tool for assessing LLM reasoning capabilities.

The dSphs around the Milky Way are commonly considered as systems that are supported by velocity dispersion against self-gravitation. They have been long accounted among the best targets to search for indirect DM signatures in the GeV-to-TeV gamma-rays due to absence of astrophysical gamma-ray foreground or background emission. We present forecasts on the sensitivity of the future CTAO for the search for annihilating or decaying DM in such targets. We perform an original selection of candidates out of the current catalog of known objects, including both classical and ultra-faint targets. For each of them, we calculate the expected amount of DM using the most updated and complete available samples of photometric and spectroscopic data of member stars, adopting a common framework of data treatment for both classes of objects. In this way, we are able to generate novel astrophysical factor profiles for general indirect DM searches that we compare with the current literature. Out of a starting sample of 64 dSphs, we highlight the 8 most promising targets - DraI, CBe, UMaII, UMi and Wil1 in the Northern hemisphere; RetII, Scl and SgrII in the Southern hemisphere - for which different DM density models (either cored or cuspy) lead to similar expectations, at variance with what happens for other DM targets - thus resulting in more robust predictions. We find that CTAO will provide the strongest limits above ~10 TeV, down to values of velocity-averaged annihilation cross section of ~5$\times 10^{-25}$ cm$^3$ s$^{-1}$ and up to decay lifetimes of ~10$^{26}$ s for combined limits on the best targets. We argue that the largest source of inaccuracy is due to the still imprecise determination of the DM content, especially for ultra-faint dSphs. We propose possible strategies of observation for CTAO, either optimized on a deep focus on the best known candidates, or on the diversification of targets.

Graham-Lovász-Pollak \cite{GL,GP} obtained the celebrated formula $$\det({\sf D}(T_{n+1}))=(-1)^nn2^{n-1},$$ for the determinant of the distance matrix ${\sf D}(T_{n+1})$ for any tree $T_{n+1}$ with $n+1$ vertices. Later, Hou and Woo \cite{HW} extended this formula to the Smith normal form (SNF) obtaining that $\SNF({\sf D}(T_{n+1}))={\sf I}_2\oplus 2{\sf I}_{n-2}\oplus [2n]$, for any tree $T_{n+1}$ with $n+1$ vertices. A $k$-{\it tree} is either a complete graph on $k$ vertices or a graph obtained from a smaller $k$-tree by adjoining a new vertex together with $k$ edges connecting it to a $k$-clique. If $\tau$ and $\tau'$ are $d$-cliques in a $k$-tree $T$, a $d$-{\it walk} between $\tau$ and $\tau'$ is a finite sequence $\tau_1\sigma_1\tau_2\sigma_2\cdots\tau_l$, where $\tau_1=\tau$, $\tau_l=\tau'$, and the $d$-cliques $\tau_i$ and $\tau_{i+1}$ are incident to the same $(d+1)$-clique $\sigma_i$. For $d\in\{1,\dots,k\}$, the $d$-{\it distance} from the $d$-cliques $\tau$ and $\tau'$ is the number of $(d+1)$-cliques in a minimum $d$-walk from $\tau$ and $\tau'$, and is denoted by $\dist^d(\tau,\tau')$. Let $c_d$ denote the number of $d$-cliques in the $k$-tree $T$. Then the $d$-distance matrix ${\sf D}^d(T)$ of the $k$-tree $T$ is the $c_d\times c_d$ matrix, indexed by the $d$-cliques of $T$, such that the $(i,j)$-entry is $0$ if $i=j$, and $\dist^d(\tau_i,\tau_j)$ otherwise. Here, we show that, for $k$ and $n$ fixed, the SNF of the $k$-distance matrix is the same for any $k$-tree with $n$ vertices. Specifically, for any $k$-tree $T_{n}$ with $n$ vertices such that $n\geq k+2$, the Smith normal form of ${\sf D}^{k}(T_{n})$ is $${\sf I}_{(k-1)(n-k)+2}\oplus (k+1){\sf I}_{n-k-2}\oplus [k(k+1)(n-k)],$$ which extends Graham-Lovász-Pollak and Hou-Woo results.

Gravitational lensing offers a powerful probe into the properties of dark matter and is crucial to infer cosmological parameters. The Legacy Survey of Space and Time (LSST) is predicted to find O(10^5) gravitational lenses over the next decade, demanding automated classifiers. In this work, we introduce GraViT, a PyTorch pipeline for gravitational lens detection that leverages extensive pretraining of state-of-the-art Vision Transformer (ViT) models and MLP-Mixer. We assess the impact of transfer learning on classification performance by examining data quality (source and sample size), model architecture (selection and fine-tuning), training strategies (augmentation, normalization, and optimization), and ensemble predictions. This study reproduces the experiments in a previous systematic comparison of neural networks and provides insights into the detectability of strong gravitational lenses on that common test sample. We fine-tune ten architectures using datasets from HOLISMOKES VI and SuGOHI X, and benchmark them against convolutional baselines, discussing complexity and inference-time analysis.

The results of a search for $\pi^0$ decays to a photon and an invisible massive dark photon at the NA62 experiment at the CERN SPS are reported. From a total of $4.12\times10^8$ tagged $\pi^0$ mesons, no signal is observed. Assuming a kinetic-mixing interaction, limits are set on the dark photon coupling to the ordinary photon as a function of the dark photon mass, improving on previous searches in the mass range 60--110 MeV/$c^2$. The present results are interpreted in terms of an upper limit of the branching ratio of the electro-weak decay $\pi^0 \to \gamma \nu \overline{\nu}$, improving the current limit by more than three orders of magnitude.

A search for the flavor-changing neutral-current decay $B^{+}\to K^{+}\nu\bar{\nu}$ is performed at the Belle II experiment at the SuperKEKB asymmetric energy electron-positron collider. The results are based on a data sample corresponding to an integrated luminosity of $63\,\mbox{fb}^{-1}$ collected at the $\Upsilon{(4S)}$ resonance and a sample of $9\,\mbox{fb}^{-1}$ collected at an energy $60\mathrm{\,Me\kern -0.1em V}$ below the resonance. A novel measurement method is employed, which exploits topological properties of the $B^{+}\to K^{+}\nu\bar{\nu}$ decay that differ from both generic bottom-meson decays and light-quark pair production. This inclusive tagging approach offers a higher signal efficiency compared to previous searches. No significant signal is observed. An upper limit on the branching fraction of $B^{+}\to K^{+}\nu\bar{\nu}$ of $4.1 \times 10^{-5}$ is set at the 90% confidence level.

The onset of generalized synchronization of chaos in directionally-coupled systems corresponds to the formation of a continuous mapping which enables one to persistently define the state of the response system from the trajectory of the drive system. The recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single-valued function. In this paper, we explore generalized synchronization in a regime where the synchronization mapping can become a multi-valued function. Specifically, we study the properties of the multi-valued mapping which occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one-to-one, and address the issues of the existence and continuity of such mappings. The basic theoretical framework underlying the considered synchronization regimes is then developed.

The NA62 experiment at the CERN SPS reports the first detection of a tagged neutrino candidate based on the data collected in 2022. The candidate consists of a $K^+ \rightarrow \mu^+ \nu_\mu$ decay where the charged particles are reconstructed and the neutrino is detected through a charged-current interaction in a liquid krypton calorimeter.

We present exponential and super factorial lower bounds on the number of Hamiltonian cycles passing through any edge of the basis graphs of a graphic, generalized Catalan and uniform matroids. All lower bounds were obtained by a common general strategy based on counting appropriated cycles of length four in the corresponding matroid basis graph.

In this paper we address the relation between the star exponentials emerging within the Deformation Quantization formalism and Feynman's path integrals associated with propagators in quantum dynamics. In order to obtain such a relation, we start by visualizing the quantum propagator as an integral transform of the star exponential by means of the symbol corresponding to the time evolution operator and, thus, we introduce Feynman's path integral representation of the propagator as a sum over all the classical histories. The star exponential thus constructed has the advantage that it does not depend on the convergence of formal series, as commonly understood within the context of Deformation Quantization. We include some basic examples to illustrate our findings, recovering standard results reported in the literature. Further, for an arbitrary finite dimensional system, we use the star exponential introduced here in order to find a particular representation of the star product which resembles the one encountered in the context of the quantum field theory for a Poisson sigma model.

Motile liquid crystal (LC) colloids show peculiar behavior due to the high sensitivity to external stimuli driven by the LC elastic and surface effects. However, few studies focus on harnessing the LC phase transitions to propel colloidal inclusions by the nematic-isotropic (NI) interface. We engineer a quasi-2D active system consisting of solid micron-sized light-absorbent platelets immersed in a thermotropic nematic LC. The platelets self-propel in the presence of light while self-inducing a localized NI phase transition. The sample's temperature, light intensity, and confinement determine three different regimes: a 2D large regime where the platelet-isotropic phase bubble is static and the NI interface remains stable; a compact motile-2D regime where the NI interface lies closer to the platelet's contour; and a motile-3D-confinement regime characterized by the emergence of multipolar configurations of the LC. We perform continuum-theory simulations that predict stationary platelet-LC states when confined in 3D. Our study in an intrinsically far-from-equilibrium landscape is crucial for designing simple synthetic systems that contribute to our understanding of harnessing liquid crystals' phase transitions to propel colloidal inclusions and trigger tunable topological reconfigurations leading to photonic responses.

In this article, we analyze the Pontryagin model adopting different geometric-covariant approaches. In particular, we focus on the manner in which boundary conditions must be imposed on the background manifold in order to reproduce an unambiguous theory on the boundary. At a Lagrangian level, we describe the symmetries of the theory and construct the Lagrangian covariant momentum map which allows for an extension of Noether's theorems. Through the multisymplectic analysis we obtain the covariant momentum map associated with the action of the gauge group on the covariant multimomenta phase-space. By performing a space plus time decomposition by means of a foliation of the appropriate bundles, we are able to recover not only the $t$-instantaneous Lagrangian and Hamiltonian of the theory, but also the generator of the gauge transformations. In the polysymplectic framework we perform a Poisson-Hamilton analysis with the help of the De Donder-Weyl Hamiltonian and the Poisson-Gerstenhaber bracket. Remarkably, as long as we consider a background manifold with boundary, in all of these geometric formulations, we are able to recover the so-called differentiability conditions as a straightforward consequence of Noether's theorem.

In this paper, we address the phase space formulation of the Jaynes-Cummings model through the explicit construction of the full Wigner function for a hybrid bipartite quantum system composed of a two-level atom and a quantized coherent field. By employing the Stratonovich-Weyl correspondence and the coadjoint orbit method, we derive an informationally complete quasi-probability distribution that captures the full dynamics of light-matter interaction. This approach provides a detailed phase space perspective of fundamental quantum phenomena such as Rabi oscillations, atomic population inversion, and entanglement generation. We further measure the purity of the reduced quantized field state by means of an appropriate Wigner function corresponding to the bosonic field part in order to investigate the entanglement dynamics of the system.

Context: Online collaborative creation of models is becoming commonplace. Collaborative modeling using chatbots and natural language may lower the barriers to modeling for users from different domains. Objective: We compare the perceived usability of two similarly online collaborative modeling tools, the SOCIO chatbot and the Creately web-based tool. Method: We conducted a crossover experiment with 66 participants. The evaluation instrument was based on the System Usability Scale (SUS). We performed a quantitative and qualitative exploration, employing inferential statistics and thematic analysis. Results: The results indicate that chatbots enabling natural language communication enhance communication and collaboration efficiency and improve the user experience. Conclusion: Chatbots need to improve guidance and help for novices, but they appear beneficial for enhancing user experience.

We present a quantum model of space charge limited current transport inside trap-free solids with planar geometry in the mean field approximation. We use a simple transformation which allows us to find the exact analytical solution for the steady state current case. We use our approach to find a Mott-Gurney like behavior and the mobility for single charge carriers in the quantum regime in solids.

Experiments with polymer latex solutions show the coexistence of order-disorder structures of macroions. Because of the large macroions' sizes, this order-disorder phase coexistence imply the existence of very long-range attractive and repulsive forces, which can not be explained in terms of conventional direct interaction potentials, which are short-range. Here we apply an integral equations theory to a simple model for colloidal dispersions, at finite concentrations, calculate the particles distribution functions and the involved effective forces. We find very long-range attractive and repulsive forces among the like-charged macroions. The distribution functions are in qualitative agreement with experimental results. The origin of these forces are discussed in terms of an energy-entropy balance.

Around 1958, Hill described how to draw the complete graph $K_n$ with [Z(n) :=1/4\lfloor \frac{n}{2}\rfloor \lfloor \frac{n-1}{2}\rfloor \lfloor \frac{n-2}{2}% \rfloor \lfloor \frac{n-3}{2}\rfloor] crossings, and conjectured that the crossing number $\crg (K_{n})$ of $K_n$ is exactly Z(n). This is also known as Guy's conjecture as he later popularized it. Towards the end of the century, substantially different drawings of $K_{n}$ with Z(n) crossings were found. These drawings are \emph{2-page book drawings}, that is, drawings where all the vertices are on a line $\ell$ (the spine) and each edge is fully contained in one of the two half-planes (pages) defined by $\ell$. The \emph{2-page crossing number} of $K_{n}$, denoted by $\nu_{2}(K_{n})$, is the minimum number of crossings determined by a 2-page book drawing of $K_{n}$. Since $\crg(K_{n}) \le\nu_{2}(K_{n})$ and $\nu_{2}(K_{n}) \le Z(n)$, a natural step towards Hill's Conjecture is the %(formally) weaker conjecture $\nu_{2}(K_{n}) = Z(n)$, popularized by Vrt'o. %As far as we know, this natural %conjecture was first raised by Imrich Vrt'o in 2007. %Prior to this paper, results known for $\nu_2(K_n)$ were basically %the same as for $\crg (K_n)$. Here In this paper we develop a novel and innovative technique to investigate crossings in drawings of $K_{n}$, and use it to prove that $\nu_{2}(K_{n}) = Z(n)$. To this end, we extend the inherent geometric definition of $k$-edges for finite sets of points in the plane to topological drawings of $K_{n}$. We also introduce the concept of ${\leq}{\leq}k$-edges as a useful generalization of ${\leq}k$-edges and extend a powerful theorem that expresses the number of crossings in a rectilinear drawing of $K_{n}$ in terms of its number of $(\le k)$-edges to the topological setting.

There are two properties shared by all known crossing-minimizing geometric drawings of $K_n$, for $n$ a multiple of 3. First, the underlying $n$-point set of these drawings has exactly $3\binom{k+2}{2}$ $(\le k)$-edges, for all 0\le k < n/3. Second, all such drawings have the $n$ points divided into three groups of equal size; this last property is captured under the concept of 3-decomposability. In this paper we show that these properties are tightly related: every $n$-point set with exactly $3\binom{k+2}{2}$ $(\le k)$-edges for all 0\le k < n/3, is 3-decomposable. As an application, we prove that the rectilinear crossing number of $K_{30}$ is 9726.

It is general wisdom that likely charged colloidal particles repel each other when suspended in liquids. This is in perfect agreement with mean field theories being developed more than 60 years ago. Accordingly, it was a big surprise when several groups independently reported long-ranged attractive components in the pair potential U(r) of equally charged colloids. This so-called like-charge attraction (LCA) was only observed in thin sample cells while the pair-interaction in unconfined suspensions has been experimentally confirmed to be entirely repulsive. Despite considerable experimental and theoretical efforts, LCA remains one of the most challenging mysteries in colloidal science. We experimentally reinvestigate the pair-potential U(r) of charged colloidal particles with digital video microscopy and demonstrate that optical distortions in the particles images lead to slightly erroneous particle positions. If not properly taken into account, this artefact pretends a minimum in U(r) which was in the past misleadingly interpreted as LCA. After correcting optical distortions we obtain entirely repulsive pair interactions which show good agreement with linearized mean field theories.

In this paper we analyze urban spatial segregation phenomenon in terms of the income distribution over a population, and inflationary parameter weighting the evolution of housing prices. For this, we develop a discrete, spatially extended model based in a multi--agent approach. In our model, the mobility of socioeconomic agents is driven only by the housing prices. Agents exchange location in order to fit their status to the cost of their housing. On the other hand, the price of a particular house changes depends on the status of its tenant, and on the neighborhood mean lodging cost, weighted by a control parameter. The agent's dynamics converges to a spatially organized configuration, whose regularity we measured by using an entropy--like indicator. With this simple model we found a nontrivial dependence of segregation on both, the initial inequality of the socioeconomic agents and the inflationary parameter. In this way we supply an explanatory model for the segregation--inequality thesis putted forward by Douglas Massey.