We show that any pseudoentangled state ensemble with a gap of $t$ bits of entropy requires $Ω(t)$ non-Clifford gates to prepare. This bound is tight up to polylogarithmic factors if linear-time quantum-secure pseudorandom functions exist. Our result follows from a polynomial-time algorithm to estimate the entanglement entropy of a quantum state across any cut of qubits. When run on an $n$-qubit state that is stabilized by at least $2^{n-t}$ Pauli operators, our algorithm produces an estimate that is within an additive factor of $\frac{t}{2}$ bits of the true entanglement entropy.

We define simple tilings in the general context of a $G$-tiling on a Riemannian homogeneous space $M$ to be tilings by Riemannian simplices. As evidence that this definition is natural, we prove that a large class of tilings of $M$ are MLD to simple ones. We demonstrate the utility of this definition by generalizing previously known results about simple tilings of Euclidean space. In particular, it is shown that a simple tiling space of a rational, connected, simply connected, nilpotent Lie group is homeomorphic to a rational tiling space, that is, a tiling space for which displacement between vertices take on rational values. Hence, such a tiling space is a fiber bundle over a nilmanifold. We further sketch a proof of the fact that there is an isomorphism between Čech cohomology and pattern equivariant cohomology of simple tilings in connected, simply connected, nilpotent Lie groups.

This paper introduces a novel control framework to address the satisfaction of multiple time-varying output constraints in uncertain high-order MIMO nonlinear control systems. Unlike existing methods, which often assume that the constraints are always decoupled and feasible, our approach can handle coupled time-varying constraints even in the presence of potential infeasibilities. First, it is shown that satisfying multiple constraints essentially boils down to ensuring the positivity of a scalar variable, representing the signed distance from the boundary of the time-varying output-constrained set. To achieve this, a single consolidating constraint is designed that, when satisfied, guarantees convergence to and invariance of the time-varying output-constrained set within a user-defined finite time. Next, a novel robust and low-complexity feedback controller is proposed to ensure the satisfaction of the consolidating constraint. Additionally, we provide a mechanism for online modification of the consolidating constraint to find a least violating solution when the constraints become mutually infeasible for some time. Finally, simulation examples of trajectory and region tracking for a mobile robot validate the proposed approach.

We study large linear structures inside sets arising in the theory of norm-attaining operators. We provide several results in the context of lineability, spaceability, maximal-spaceability, and $(α, β)$-spaceability for sets of non-norm-attaining bounded linear operators whenever such sets are nonempty. To be more specific, we show that if $Y$ is a strictly convex renorming of $c_0 (Γ)$, then the set $$ \mathcal{L}(c_0 (Γ),Y)\setminus \overline{\text{NA} (c_0 (Γ),Y)} $$ is $2^{|Γ|}$-spaceable. We also prove that $$ \mathcal{L}(d_* (w,1) ,\ell_p )\setminus \overline{\text{NA} (d_* (w,1),\ell_p )} $$ is maximal-spaceable. Finally, we establish that whenever the set of non-norm-attaining operators from a Banach space $X$ into $\ell_p (Γ)$ (respectively, $c_0 (Γ)$) is nonempty, it contains a subspace linearly isometric to $\ell_p(Γ)$ (respectively, $c_0 (Γ)$). These results extend and complement several known results in the literature concerning large linear structures in sets of non-norm-attaining operators. Our results are obtained in a more general framework involving group-invariant operators, which allows us to treat classical spaces of operators as special cases.

Located in Southern Europe, the Drina River Basin is shared between Bosnia and Herzegovina, Montenegro, and Serbia. The power sectors of the three countries have an exceptionally high dependence on coal for power generation. In this paper, we analyse different development pathways for achieving climate neutrality in these countries and explore the potential of variable renewable energy (VRE) and its role in power sector decarbonization. We investigate whether hydro and non-hydro renewables can enable a net-zero transition by 2050 and how VRE might affect the hydropower cascade shared by the three countries. The Open-Source Energy Modelling System (OSeMOSYS) was used to develop a model representation of the countries' power sectors. Findings show that the renewable potential of the countries is a significant 94.4 GW. This potential is 68% higher than previous assessments have shown. Under an Emission Limit scenario assuming net zero by 2050, 17% of this VRE potential is utilized to support the decarbonization of the power sectors. Additional findings show a limited impact of VRE technologies on total power generation output from the hydropower cascade. However, increased solar deployment shifts the operation of the cascade to increased short-term balancing, moving from baseload to more responsive power generation patterns. Prolonged use of thermal power plants is observed under scenarios assuming high wholesale electricity prices, leading to increased emissions. Results from scenarios with low cost of electricity trade suggest power sector developments that lead to decreased energy security.

How does quantum chaos lead to rapid scrambling of information as well as systematic errors across a system when one introduces perturbations in the dynamics? What are its consequences for the reliability of quantum simulations and quantum information processing? We employ continuous measurement quantum tomography as a paradigm to study these questions. The measurement record is generated as a sequence of expectation values of a Hermitian observable evolving under repeated application of the Floquet map of the quantum kicked top. We construct a quantity to capture the scrambling of systematic errors, an out-of-time-ordered correlator (OTOC), that serves as a signature of chaos and quantifies the spread of errors. We show that the spread of errors, as quantified by the OTOC, is related to the operator Loschmidt echo (OLE), which is defined as the Hilbert-Schmidt inner product of the operators $\mathcal{O}_n$ and $\mathcal{O'}_n$ generated from repeated application of the Floquet map for ideal (unperturbed) dynamics and the \emph{true} (perturbed) dynamics, respectively. This also gives us an operational interpretation of the Loschmidt echo for operators by connecting it to the performance of quantum tomography. We show how our results demonstrate not only a link between LE and scrambling of errors different than previous studies, but that such a link can have operational consequences in quantum information processing.

In this work, we demonstrate that use of dimethylformamide (DMF) as a solvent leads to better dispersion of graphene nanoplatelets in epoxy matrix compared to acetone solvent, in turn leading to higher thermal conductivity epoxy-graphene nanocomposites. While role of solvents in enabling superior mechanical properties has been addressed before, outlined study is the first to address the effect of solvents on thermal conductivity enhancement and provides novel pathways for achieving high thermal conductivity polymer composite materials. Uniform dispersion of graphene nanoparticles into epoxy can improve thermal contact with polymer leading to superior interface thermal conductance between polymer matrix and graphene. Organic solvents are typically employed to achieve efficient dispersion of graphene into the epoxy matrix. In this study, we compare the effect of two organic solvents, dimethylformamide (DMF) and acetone, in terms of their efficiency in dispersing graphene into the epoxy matrix and their effect on enhancing thermal conductivity of the composite. We find that polymer-graphene composites made with DMF solvent show 44% higher thermal conductivity compared to those made using acetone at 7 weight% filler composition. Laser scanning confocal microscopy (LSCM) imaging reveals that graphene-epoxy composites, prepared using DMF as solvent, exhibit more uniform dispersion of graphene-nanoplatelets compared to the case of acetone with acetone-based samples exhibiting up to 211% larger graphene agglomerations. Comparison with effective medium theory reveals an almost 35% lower interface thermal resistance between graphene and epoxy for DMF relative to acetone prepared composite. These results provide fundamentally new avenues to achieve higher thermal conductivity graphene-epoxy composites, of key importance for a wide range of thermal management technologies.

We investigate the cosmology of mini Primordial Black Holes (PBHs) produced by large density perturbations that collapse during a stiff fluid domination phase. Such a phase can be realized by a runaway-inflaton model that crosses an inflection point or a sharp feature at the last stage of inflation. Mini PBHs evaporate promptly and reheat the early universe. In addition, we examine two notable implications of this scenario: the possible presence of PBH evaporation remnants in galaxies and a non-zero residual potential energy density for the runaway inflaton that might play the role of the dark energy. We specify the parameter space that this scenario can be realized and we find that a transit PBH domination phase is necessary due to gravitational wave (GW) constraints. A distinct prediction of the scenario is a compound GW signal that might be probed by current and future experiments. We also demonstrate our results employing an explicit inflation model.

Moving window and hot spot detection analyses are statistical methods used to analyze point patterns within a given area. Such methods have been used to successfully detect clusters of point events such as car thefts or incidences of cancer. Yet, these methods do not account for the connections between individual events, such as social ties within a neighborhood. This paper presents two GIS methods, EdgeScan and NDScan, for capturing areas with high and low levels of local social connections. Both methods are moving window processes that count the number of edges and network density, respectively, in a given focal area (window area). The focal window attaches resultant EdgeScan and NDScan statistics to nodes at the center of the focal window area. We implement these methods on a case study of 1960s connections between members of the Mafia in New York City. We use various definitions of a focal neighborhood including Euclidean, Manhattan and K Nearest Neighbor (KNN) definitions. We find that KNN tends to overstate the values of local networks, and that there is more variation in outcome values for nodes on the periphery of the study area. We find that, location-wise, EdgeScan and NDScan hot spots differ from traditional spatial hot spots in the study area. These methods can be extended to future studies that detect local triads and motifs, which can capture the local network structure in more detail.

Motivated by the Pierce-Birkhoff conjecture, we launch an extension program for single variable expansivity theory. We study this notion under tuples of polynomials in the ring $\mathbb{R}[x_1,x_2,\ldots,x_n]$. As an application, we develop some class of inequalities to study the Pierce-Birkhoff conjecture.

We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can benefit from an analysis that takes into account the distributional changes across environments. In particular, it is useful to distinguish between stable and unstable predictors, i.e., predictors which have a fixed or a changing functional dependence on the response, respectively. We introduce stabilized regression which explicitly enforces stability and thus improves generalization performance to previously unseen environments. Our work is motivated by an application in systems biology. Using multiomic data, we demonstrate how hypothesis generation about gene function can benefit from stabilized regression. We believe that a similar line of arguments for exploiting heterogeneity in data can be powerful for many other applications as well. We draw a theoretical connection between multi-environment regression and causal models, which allows to graphically characterize stable versus unstable functional dependence on the response. Formally, we introduce the notion of a stable blanket which is a subset of the predictors that lies between the direct causal predictors and the Markov blanket. We prove that this set is optimal in the sense that a regression based on these predictors minimizes the mean squared prediction error given that the resulting regression generalizes to unseen new environments.

Consider rectangular matrices over a commutative ring R. Assume the ideal of maximal minors factorizes, I_m(A)=J_1*J_2. When is A left-right equivalent to a block-diagonal matrix? (When does the module/sheaf Coker(A) decompose as the corresponding direct sum?) If R is not an elementary divisor ring (i.e. not a close relative of a principal ideal ring) one needs additional assumptions on A. No necessary and sufficient criterion for such block-diagonal reduction is known. In this part we establish the following: * The persistence of (in)decomposability under the change of rings. For example, the passage to Noetherian/local/complete rings, the decomposability of A over a graded ring R vs the decomposability of Coker(A) locally at the points of Proj(R), the restriction to a subscheme in Spec(R). * The necessary and sufficient condition for decomposability of square matrices in the case: det(A)=f_1*f_2 is not a zero divisor and f_1,f_2 are co-prime. As an immediate application we give criteria of simultaneous (block-)diagonal reduction for tuples of matrices over a field, i.e. linear determinantal representations.

The completion of the GALEX All-Sky Survey in the ultraviolet allows activity measurements to be acquired for many more stars than is possible with the limited sensitivity of ROSAT or the limited sky coverage of Chandra, XMM, or spectroscopic surveys for line emission in the optical or ultraviolet. We have explored the use of GALEX photometry as an activity indicator, using as a calibration sample stars within 50 pc, representing the field, and in selected nearby associations, representing the youngest stages of stellar evolution. We present preliminary relations between UV flux and the optical activity indicator R'_HK and between UV flux and age. We demonstrate that far-UV (FUV, 1350-1780Å) excess flux is roughly proportional to R'_HK. We also detect a correlation between near-UV (NUV, 1780-2830Å) flux and activity or age, but the effect is much more subtle, particularly for stars older than than ~0.5-1 Gyr. Both the FUV and NUV relations show large scatter, ~0.2 mag when predicting UV flux, ~0.18 dex when predicting R'_HK, and ~0.4 dex when predicting age. This scatter appears to be evenly split between observational errors in current state-of-the-art data and long-term activity variability in the sample stars.

We have carried out a Galaxy Evolution Explorer (GALEX) Cycle 1 guest investigator program covering 56 square degrees near the Taurus T association and 12 square degrees along the northern edge of the Upper Scorpius OB association. We combined photometry in the GALEX FUV and NUV bands with data from the Two Micron All Sky Survey to identify candidate young (<100 Myr old) stars as those with an ultraviolet excess relative to older main sequence stars. Follow-up spectroscopy of a partial sample of these candidates suggest 5 new members of Taurus, with 8-20 expected from additional observations, and 5 new members of Upper Scorpius, with 3-6 expected from additional observations. These candidate new members appear to represent a distributed, non-clustered population in either region, although our sample statistics are as of yet too poor to constrain the nature or extent of this population. Rather, our study demonstrates the ability of GALEX observations to identify young stellar populations distributed over a wide area of the sky. We also highlight the necessity of a better understanding of the Galactic ultraviolet source population to support similar investigations. In particular, we report a large population of stars with an ultraviolet excess but no optical indicators of stellar activity or accretion, and briefly argue against several interpretations of these sources.

The search for binarity in AGB stars is of critical importance for our understanding of how planetary nebulae acquire the dazzling variety of aspherical shapes which characterises this class. However, detecting binary companions in such stars has been severely hampered due to their extreme luminosities and pulsations. We have carried out a small imaging survey of AGB stars in ultraviolet light (using GALEX) where these cool objects are very faint, in order to search for hotter companions. We report the discovery of significant far-ultraviolet excesses towards nine of these stars. The far-ultraviolet excess most likely results either directly from the presence of a hot binary companion, or indirectly from a hot accretion disk around the companion.