Subset Sampling and Its Extensions

This paper studies the \emph{subset sampling} problem. The input is a set $\mathcal{S}$ of $n$ records together with a function $\textbf{p}$ that assigns each record $v\in\mathcal{S}$ a probability $\textbf{p}(v)$. A query returns a random subset $X$ of $\mathcal{S}$, where each record $v\in\mathcal{S}$ is sampled into $X$ independently with probability $\textbf{p}(v)$. The goal is to store $\mathcal{S}$ in a data structure to answer queries efficiently. If $\mathcal{S}$ fits in memory, the problem is interesting when $\mathcal{S}$ is dynamic. We develop a dynamic data structure with $\mathcal{O}(1+\mu_{\mathcal{S}})$ expected \emph{query} time, $\mathcal{O}(n)$ space and $\mathcal{O}(1)$ amortized expected \emph{update}, \emph{insert} and \emph{delete} time, where $\mu_{\mathcal{S}}=\sum_{v\in\mathcal{S}}\textbf{p}(v)$. The query time and space are optimal. If $\mathcal{S}$ does not fit in memory, the problem is difficult even if $\mathcal{S}$ is static. Under this scenario, we present an I/O-efficient algorithm that answers a \emph{query} in $\mathcal{O}\left((\log^*_B n)/B+(\mu_\mathcal{S}/B)\log_{M/B} (n/B)\right)$ amortized expected I/Os using $\mathcal{O}(n/B)$ space, where $M$ is the memory size, $B$ is the block size and $\log^*_B n$ is the number of iterative $\log_2(.)$ operations we need to perform on $n$ before going below $B$. In addition, when each record is associated with a real-valued key, we extend the \emph{subset sampling} problem to the \emph{range subset sampling} problem, in which we require that the keys of the sampled records fall within a specified input range $[a,b]$. For this extension, we provide a solution under the dynamic setting, with $\mathcal{O}(\log n+\mu_{\mathcal{S}\cap[a,b]})$ expected \emph{query} time, $\mathcal{O}(n)$ space and $\mathcal{O}(\log n)$ amortized expected \emph{update}, \emph{insert} and \emph{delete} time.Comment: 17 page

Thermodynamics of an Exactly Solvable Model for Superconductivity in a Doped Mott Insulator

Computing superconducting properties starting from an exactly solvable model for a doped Mott insulator stands as a grand challenge. We have recently shown that this can be done starting from the Hatsugai-Kohmoto (HK) model which can be understood generally as the minimal model that breaks the non-local $\mathbb Z_2$ symmetry of a Fermi liquid, thereby constituting a new quartic fixed point for Mott physics [Phillips et al., Nature Physics 16, 1175 (2020); Huang et al., Nature Physics (2022)]. In the current work, we compute the thermodynamics, condensation energy, and electronic properties such as the NMR relaxation rate $1/T_1$ and ultrasonic attenuation rate. Key differences arise with the standard BCS analysis from a Fermi liquid: 1) the free energy exhibits a local minimum at $T_p$ where the pairing gap turns on discontinuously above a critical value of the repulsive HK interaction, thereby indicating a first-order transition, 2) a tri-critical point emerges, thereby demarcating the boundary between the standard second-order superconducting transition and the novel first-order regime, 3) Mottness changes the sign of the quartic coefficient in the Landau-Ginzburg free-energy fuctional relative to that in BCS, 4) as this obtains in the strongly interacting regime, it is Mott physics that underlies the generic first-order transition, 5) the condensation energy exceeds that in BCS theory suggesting that multiple Mott bands might be a way of enhancing superconducting, 6) the heat-capacity jump is non-universal and increases with the Mott scale, 7) Mottness destroys the Hebel-Slichter peak in NMR, and 8) Mottness enhances the fall-off of the ultrasonic attenuation at the pairing temperature $T_p$. As several of these properties are observed in the cuprates, our analysis here points a way forward in computing superconducting properties of strongly correlated electron matter.Comment: accepted in PR

Dynamic Cycling of t-SNARE Acylation Regulates Platelet Exocytosis

Platelets regulate vascular integrity by secreting a host of molecules that promote hemostasis and its sequelae. Given the importance of platelet exocytosis, it is critical to understand how it is controlled. The t-SNAREs, SNAP-23 and syntaxin-11, lack classical transmembrane domains (TMDs), yet both are associated with platelet membranes and redistributed into cholesterol-dependent lipid rafts when platelets are activated. Using metabolic labeling and hydroxylamine (HA)/HCl treatment, we showed that both contain thioester-linked acyl groups. Mass spectrometry mapping further showed that syntaxin-11 was modified on cysteine 275, 279, 280, 282, 283, and 285, and SNAP-23 was modified on cysteine 79, 80, 83, 85, and 87. Interestingly, metabolic labeling studies showed incorporation of [3H]palmitate into the t-SNAREs increased although the protein levels were unchanged, suggesting that acylation turns over on the two t-SNAREs in resting platelets. Exogenously added fatty acids did compete with [3H]palmitate for t-SNARE labeling. To determine the effects of acylation, we measured aggregation, ADP/ATP release, as well as P-selectin exposure in platelets treated with the acyltransferase inhibitor cerulenin or the thioesterase inhibitor palmostatin B. We found that cerulenin pretreatment inhibited t-SNARE acylation and platelet function in a dose- and time-dependent manner whereas palmostatin B had no detectable effect. Interestingly, pretreatment with palmostatin B blocked the inhibitory effects of cerulenin, suggesting that maintaining the acylation state is important for platelet function. Thus, our work shows that t-SNARE acylation is actively cycling in platelets and suggests that the enzymes regulating protein acylation could be potential targets to control platelet exocytosis in vivo

Steroid saponins and other constituents from the rhizome of Trillium tschonoskii Maxim and their cytotoxic activity

Fourteen compounds were isolated from the rhizome of Trillium tschonoskii Maxim. By spectroscopic analysis, these compounds were established as Gracillin (1), Paris saponins V (2), Paris saponins VI (3), Paris saponins H (4), Paris saponins VII (5), (25R)-17α-hydroxy-5-en-3-O-a-L-arabinofuranosyl-(1→2)-β-Dglucopyranoside (6), (25R)-26-[β-D-glucopyanosyl]-17α,22β-dihydroxy-5-en-3-O-a-L-rhamnopyranosyl- (1→2)-β-D-glucopyranoside (7), Kaempferol-3-O-β-D-rutinoside (8), Quercetin (9), Quercetin-3-O-β-D-galactoside (10), Daucosterol (11), Stigmasterol-3-O-β-D-glucopyranoside (12), 3, 5-Di-O-caffeoyl quinic acid (13), and n-Hexadecanoic acid (14). By GC-MS analysis of the CH2Cl2 extract from Trillium tschonoskii Maxim, twenty compouns were identified, representing 91 % of the area. The cytotoxicity of compounds 1-14 on mouse A549 cells were evaluated.Colegio de Farmacéuticos de la Provincia de Buenos Aire

Exact solution for finite center-of-mass momentum Cooper pairing

Pair density waves (PDWs) are superconducting states formed by ``Cooper pairs" of electrons containing a non-zero center-of-mass momentum. They are characterized by a spatially modulated order parameter and may occur in a variety of emerging quantum materials such as cuprates, transition metal dichalcogenides (TMDs) and Kagome metals. Despite extensive theoretical and numerical studies seeking PDWs in a variety of lattices and interacting settings, there is currently no generic and robust mechanism that favors a modulated solution of the superconducting order parameter in the presence of time reversal symmetry. Here, we study the problem of two electrons subject to an anisotropic ($d$-wave) attractive potential. We solve the two-body Schrodinger wave equation exactly to determine the pair binding energy as a function of the center-of-mass momentum. We find that a modulated (finite momentum) pair is favored over a homogeneous (zero momentum) solution above a critical interaction. Using this insight from the exact two-body solution, we construct a BCS-like variational many-body wave function and calculate the free energy and superconducting gap as a function of the center-of-mass momentum. A zero temperature analysis of the energy shows that the conclusions of the two-body problem are robust in the many-body limit. Our results lay the theoretical and microscopic foundation for the existence of PDWs.Comment: 24 pages, 6 figure

Steroid saponins and other constituents from the rhizome of Trillium tschonoskii Maxim and their cytotoxic activity

Fourteen compounds were isolated from the rhizome of Trillium tschonoskii Maxim. By spectroscopic analysis, these compounds were established as Gracillin (1), Paris saponins V (2), Paris saponins VI (3), Paris saponins H (4), Paris saponins VII (5), (25R)-17α-hydroxy-5-en-3-O-a-L-arabinofuranosyl-(1→2)-β-Dglucopyranoside (6), (25R)-26-[β-D-glucopyanosyl]-17α,22β-dihydroxy-5-en-3-O-a-L-rhamnopyranosyl- (1→2)-β-D-glucopyranoside (7), Kaempferol-3-O-β-D-rutinoside (8), Quercetin (9), Quercetin-3-O-β-D-galactoside (10), Daucosterol (11), Stigmasterol-3-O-β-D-glucopyranoside (12), 3, 5-Di-O-caffeoyl quinic acid (13), and n-Hexadecanoic acid (14). By GC-MS analysis of the CH2Cl2 extract from Trillium tschonoskii Maxim, twenty compouns were identified, representing 91 % of the area. The cytotoxicity of compounds 1-14 on mouse A549 cells were evaluated.Colegio de Farmacéuticos de la Provincia de Buenos Aire

AceGPT, Localizing Large Language Models in Arabic

This paper explores the imperative need and methodology for developing a localized Large Language Model (LLM) tailored for Arabic, a language with unique cultural characteristics that are not adequately addressed by current mainstream models like ChatGPT. Key concerns additionally arise when considering cultural sensitivity and local values. To this end, the paper outlines a packaged solution, including further pre-training with Arabic texts, supervised fine-tuning (SFT) using native Arabic instructions and GPT-4 responses in Arabic, and reinforcement learning with AI feedback (RLAIF) using a reward model that is sensitive to local culture and values. The objective is to train culturally aware and value-aligned Arabic LLMs that can serve the diverse application-specific needs of Arabic-speaking communities. Extensive evaluations demonstrated that the resulting LLM called `AceGPT' is the SOTA open Arabic LLM in various benchmarks, including instruction-following benchmark (i.e., Arabic Vicuna-80 and Arabic AlpacaEval), knowledge benchmark (i.e., Arabic MMLU and EXAMs), as well as the newly-proposed Arabic cultural \& value alignment benchmark. Notably, AceGPT outperforms ChatGPT in the popular Vicuna-80 benchmark when evaluated with GPT-4, despite the benchmark's limited scale. % Natural Language Understanding (NLU) benchmark (i.e., ALUE) Codes, data, and models are in https://github.com/FreedomIntelligence/AceGPT.Comment: https://github.com/FreedomIntelligence/AceGP