Batch effects pose a significant challenge in the analysis of single-cell omics data, introducing technical artifacts that confound biological signals. While various computational methods have achieved empirical success in correcting these effects, they lack the formal theoretical guarantees required to assess their reliability and generalization. To bridge this gap, we introduce Mixture-Model-based Data Harmonization (MoDaH), a principled batch correction algorithm grounded in a rigorous statistical framework. Under a new Gaussian-mixture-model with explicit parametrization of batch effects, we establish the minimax optimal error rates for batch correction and prove that MoDaH achieves this rate by leveraging the recent theoretical advances in clustering data from anisotropic Gaussian mixtures. This constitutes, to the best of our knowledge, the first theoretical guarantee for batch correction. Extensive experiments on diverse single-cell RNA-seq and spatial proteomics datasets demonstrate that MoDaH not only attains theoretical optimality but also achieves empirical performance comparable to or even surpassing those of state-of-the-art heuristics (e.g., Harmony, Seurat-V5, and LI
In multi-access wireless networks, transmission scheduling is a key component that determines the efficiency and fairness of wireless spectrum allocation. At one extreme, greedy opportunistic scheduling that allocates airtime to the user with the largest instantaneous channel gain achieves the optimal spectrum efficiency and transmission reliability but the poorest user-level fairness. At the other extreme, fixed TDMA scheduling achieves the fairest airtime allocation but the lowest spectrum efficiency and transmission reliability. To balance the two competing objectives, extensive research efforts have been spent on designing opportunistic scheduling schemes that reach certain tradeoff points between the two extremes. In this paper and in contrast to the conventional wisdom, we find that in relay-assisted cellular networks, fixed TDMA achieves the same optimal diversity gain as greedy opportunistic scheduling. In addition, by incorporating very limited opportunism, a simple relaxed-TDMA scheme asymptotically achieves the same optimal system reliability in terms of outage probability as greedy opportunistic scheduling. This reveals a surprising fact: transmission reliability and us
Since the 1990s, AI systems have achieved superhuman performance in major zero-sum games where "winning" has an unambiguous definition. However, most social interactions are mixed-motive games, where measuring the performance of AI systems is a non-trivial task. In this paper, I propose a novel benchmark called super-Nash performance to assess the performance of AI systems in mixed-motive settings. I show that a solution concept called optimin achieves super-Nash performance in every n-person game, i.e., for every Nash equilibrium there exists an optimin where every player not only receives but also guarantees super-Nash payoffs even if the others deviate unilaterally and profitably from the optimin.
Diversity order is an important measure for the performance of communication systems over MIMO fading channels. In this paper, we prove that in MIMO multiple access systems (or MIMO point-to-point systems with V-BLAST transmission), lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, we prove that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity.
There is the long-standing assumption that radio communication in the range of hundreds of meters needs to consume mWs of power at the transmitting device. In this paper, we demonstrate that this is not necessarily the case for some devices equipped with backscatter radios. We present LoRea an architecture consisting of a tag, a reader and multiple carrier generators that overcomes the power, cost and range limitations of existing systems such as Computational Radio Frequency Identification~(CRFID). LoRea achieves this by: First, generating narrow-band backscatter transmissions that improve receiver sensitivity. Second, mitigating self-interference without the complex designs employed on RFID readers by keeping carrier signal and backscattered signal apart in frequency. Finally, decoupling carrier generation from the reader and using devices such as WiFi routers and sensor nodes as a source of the carrier signal. An off-the-shelf implementation of LoRea costs 70 USD, a drastic reduction in price considering commercial RFID readers cost 2000 USD. LoRea's range scales with the carrier strength, and proximity to the carrier source and achieves a maximum range of 3.4 kilometre when the
For a discrete memoryless channel with non-causal state information available only at the encoder, it is well-known that Gelfand-Pinsker coding achieves its capacity. In this paper, we analyze Gelfand-Pinsker coding scheme and capacity to bring out further understandings. We show that Gelfand-Pinsker capacity is equal to the interference-free capacity. Thus the capacity of a channel with non-causal state information available only at the encoder is the same as if the state information is also available at the decoder. Furthermore, the capacity-achieving conditional input distributions in these two cases are the same. This lets us connect the studied channel with state to the multiple access channel (MAC) with correlated sources and show that under certain conditions, the receiver can decode both the message and the state information. This dual decoding can be obtained in particular if the state sequences come from a known codebook with rate satisfying a simple constraint. In such a case, we can modify Gelfand-Pinsker coding by pre-building multiple codebooks of input sequences $X^n$, each codebook is for a given state sequence $S^n$, upon generating the auxiliary $U^n$ sequences. T
We aim at finding the minimal set of fragments which achieves maximal parse accuracy in Data Oriented Parsing. Experiments with the Penn Wall Street Journal treebank show that counts of almost arbitrary fragments within parse trees are important, leading to improved parse accuracy over previous models tested on this treebank (a precision of 90.8% and a recall of 90.6%). We isolate some dependency relations which previous models neglect but which contribute to higher parse accuracy.
We study the phase synchronization problem with noisy measurements $Y=z^*z^{*H}+σW\in\mathbb{C}^{n\times n}$, where $z^*$ is an $n$-dimensional complex unit-modulus vector and $W$ is a complex-valued Gaussian random matrix. It is assumed that each entry $Y_{jk}$ is observed with probability $p$. We prove that an SDP relaxation of the MLE achieves the error bound $(1+o(1))\frac{σ^2}{2np}$ under a normalized squared $\ell_2$ loss. This result matches the minimax lower bound of the problem, and even the leading constant is sharp. The analysis of the SDP is based on an equivalent non-convex programming whose solution can be characterized as a fixed point of the generalized power iteration lifted to a higher dimensional space. This viewpoint unifies the proofs of the statistical optimality of three different methods: MLE, SDP, and generalized power method. The technique is also applied to the analysis of the SDP for $\mathbb{Z}_2$ synchronization, and we achieve the minimax optimal error $\exp\left(-(1-o(1))\frac{np}{2σ^2}\right)$ with a sharp constant in the exponent.
We show that for a generic real or complex-valued compactly supported potential, the corresponding Schroedinger operator achieves maximal resonance density, in the sense that its integrated resonance counting function achieves the optimal asymptotic upper bound. For odd dimensions this follows from results of Dinh-Vu once we adapt an argument of Christiansen Hislop. The proof for even dimensions constitutes the bulk of the paper, and we prove several new results on resonances which have analogues in the odd dimensional case. This includes a sharp upper bound on the integrated resonance counting function for any compactly support potential, a proof that the characteristic function of a ball has resonance counting function which achieves the optimal upper bound, and an even-dimensional analogue of the result of Dinh-Vu on asymptotics of the resonance counting functions for complements of pluripolar subsets of analytic families of potentials. We use the characterization of resonances as zeros of certain Fredholm determinant functions related to the scattering matrix, allowing us to apply techniques and results from the theories of one and several complex variables. Our proof that the
This paper proposes a coding framework for capacity-region-achieving sparse regression (SR) codes over MIMO multiple-access channels (MIMO-MAC), where a single SR code is used for each user at the transmitter. With random semi-unitary dictionary matrices applied for encoding, multiple-access OAMP (MA-OAMP) enables reliable parallel interference cancellation (PIC) at the receiver. Theoretically, an optimal coding principle with the MA-OAMP receiver, which achieves the sum capacity and, in combination with time sharing, achieves the entire capacity region, is established as the guiding principle for designing capacity-region-achieving codes. Accordingly, a coding scheme for capacity-region-achieving SR codes is proposed via proper power allocation over the position-modulated signals.
Translating natural language to SQL (Text-to-SQL) is a critical challenge in both database research and data analytics applications. Recent efforts have focused on enhancing SQL reasoning by developing large language models and AI agents that decompose Text-to-SQL tasks into manually designed, step-by-step pipelines. However, despite these extensive architectural engineering efforts, a significant gap remains: even state-of-the-art (SOTA) AI agents have not yet achieved the human-level accuracy on the BIRD benchmark. In this paper, we show that closing this gap does not require further architectural complexity, but rather clean training data to improve SQL reasoning of the underlying models. We introduce ReViSQL, a streamlined framework that achieves human-level accuracy on BIRD for the first time. Instead of complex AI agents, ReViSQL leverages reinforcement learning with verifiable rewards (RLVR) on BIRD-Verified, a dataset we curated comprising 2.5k verified Text-to-SQL instances based on the BIRD Train set. To construct BIRD-Verified, we design a data correction and verification workflow involving SQL experts. We identified and corrected data errors in 61.1% of a subset of BIRD
We present Supernova, a 650M-parameter decoder-only transformer that demonstrates how careful architectural design and tokenization innovation can achieve the performance of larger models while maintaining computational efficiency. Our architecture combines Rotary Positional Embeddings (RoPE), Grouped Query Attention (GQA) with a 3:1 compression ratio, RMSNorm for computational efficiency, and SwiGLU activation functions. A critical innovation is our custom 128,000-vocabulary byte-level BPE tokenizer, which achieves state-of-the-art compression performance. Through detailed analysis, we show that Supernova achieves 90% of the performance of 1B-parameter models while using 35% fewer parameters and requiring only 100B training tokens--an order of magnitude less than competing models. Our findings challenge the prevailing scaling paradigm, demonstrating that architectural efficiency and tokenization quality can compensate for reduced parameter counts.
Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for achieving quantum advantage in combinatorial optimization. However, its variational framework presents a long-standing challenge in selecting circuit parameters. In this work, we prove that the energy expectation produced by QAOA can be expressed as a trigonometric function of the final-level mixer parameter. Leveraging this insight, we introduce Penta-O, a level-wise parameter-setting strategy that eliminates the classical outer loop, maintains minimal sampling overhead, and ensures non-decreasing performance. This method is broadly applicable to the generic quadratic unconstrained binary optimization formulated as the Ising model. For a $p$-level QAOA, Penta-O achieves an unprecedented quadratic time complexity of $\mathcal{O}(p^2)$ and a sampling overhead proportional to $5p+1$. Through experiments and simulations, we demonstrate that QAOA enhanced by Penta-O achieves near-optimal performance with exceptional circuit depth efficiency. Our work provides a versatile tool for advancing variational quantum algorithms.
Within the family of guessing-based decoding algorithms, ordered reliability bits GRAND (ORBGRAND) has attracted considerable attention due to its efficient use of soft information and suitability for hardware implementation. It has also been shown that ORBGRAND achieves a rate very close to the capacity of an additive white Gaussian noise channel under antipodal signaling. In this work, it is further established that, for general binary-input memoryless channels under symmetric input distribution, via suitably companding the ranks in ORBGRAND according to the inverse cumulative distribution function (CDF) of channel reliability, the resulting CDF-ORBGRAND algorithm exactly achieves the mutual information, i.e., the symmetric capacity. This result is then applied to bit-interleaved coded modulation (BICM) systems to handle high-order input constellations. Via considering the effects of mismatched decoding due to both BICM and ORBGRAND, it is shown that CDF-ORBGRAND is capable of achieving the BICM capacity, which was initially derived in the literature by treating BICM as a set of independent parallel channels.
A significant connection exists between the controllability of dynamical systems and the approximation capabilities of neural networks, where residual networks and vanilla feedforward neural networks can both be regarded as numerical discretizations of the flow maps of dynamical systems. Leveraging the expressive power of neural networks, prior works have explored various control families $\mathcal{F}$ that enable the flow maps of dynamical systems to achieve either the universal approximation property (UAP) or the universal interpolation property (UIP). For example, the control family $\mathcal{F}_\text{ass}({\mathrm{ReLU}})$, consisting of affine maps together with a specific nonlinear function ReLU, achieves UAP; while the affine-invariant nonlinear control family $\mathcal{F}_{\mathrm{aff}}(f)$ containing a nonlinear function $f$ achieves UIP. However, UAP and UIP are generally not equivalent, and thus typically need to be studied separately with different techniques. In this paper, we investigate more general control families, including $\mathcal{F}_\text{ass}(f)$ with nonlinear functions $f$ beyond ReLU, the diagonal affine-invariant family $\mathcal{F}_{\mathrm{diag}}(f)$, a
Multinomial Logistic Bandits have recently attracted much attention due to their ability to model problems with multiple outcomes. In this setting, each decision is associated with many possible outcomes, modeled using a multinomial logit function. Several recent works on multinomial logistic bandits have simultaneously achieved optimal regret and computational efficiency. However, motivated by real-world challenges and practicality, there is a need to develop algorithms with limited adaptivity, wherein we are allowed only $M$ policy updates. To address these challenges, we present two algorithms, B-MNL-CB and RS-MNL, that operate in the batched and rarely-switching paradigms, respectively. The batched setting involves choosing the $M$ policy update rounds at the start of the algorithm, while the rarely-switching setting can choose these $M$ policy update rounds in an adaptive fashion. Our first algorithm, B-MNL-CB extends the notion of distributional optimal designs to the multinomial setting and achieves $\tilde{O}(\sqrt{T})$ regret assuming the contexts are generated stochastically when presented with $Ω(\log \log T)$ update rounds. Our second algorithm, RS-MNL works with advers
From the standpoint of applied ontology, the problem of understanding and modeling causation has been recently challenged on the premise that causation is real. As a consequence, the following three results were obtained: (1) causation can be understood via the notion of systemic function; (2) any cause can be decomposed using only four subfunctions, namely Achieves, Prevents, Allows, and Disallows; and (3) the last three subfunctions can be defined in terms of Achieves alone. It follows that the essence of causation lies in a single function, namely Achieves. It remains to elucidate the nature of the Achieves function, which has been elaborated only partially in the previous work. In this paper, we first discuss a couple of underlying policies in the above-mentioned causal theory since these are useful in the discussion, then summarize the results obtained in the former paper, and finally reveal the nature of Achieves giving a complete solution to the problem of what causation is.
We wish to generate list-decodable codes over small alphabets using as little randomness as possible. Specifically, we hope to generate codes achieving what we term the Elias bound, which means that they are $(ρ,L)$-list-decodable with rate $R \geq 1-h(ρ)-O(1/L)$. A long line of work shows that uniformly random linear codes (RLCs) achieve the Elias bound: hence, we know $O(n^2)$ random bits suffice. Prior works demonstrate that just $O(Ln)$ random bits suffice, via puncturing of low-bias codes. These recent constructions are combinatorial. We provide two new constructions, which are algebraic. Compared to prior works, our constructions are simpler and more direct. Furthermore, our codes are designed in such a way that their duals are also quite easy to analyze. Our first construction -- which can be seen as a generalization of the Wozencraft ensemble -- achieves the Elias bound and consumes $Ln$ random bits. Additionally, its dual code achieves the GV-bound with high probability, and both the primal and dual admit quasilinear-time encoding algorithms. The second construction consumes $2nL$ random bits and yields a code where both it and its dual achieve the Elias bound. As we discu
We study the fair allocation problem of indivisible items with subsidy. In this paper, we focus on the notion of fairness - equitability (EQ), which requires that items be allocated such that all agents value the bundle they receive equally. First, we study the upper bounds of the minimum required subsidy to achieve EQ in different item settings and provide the corresponding lower bounds. Second, we consider the bounded subsidy for achieving EQ and another popular notion of fairness - envy-freeness (EF), and give a characterization of allocations that can achieve both EQ and EF. Finally, we analyze the bounds of subsidy of allocations achieving fairness and efficiency (utilitarian social welfare or Nash welfare) and design several polynomial-time algorithms to compute the desired allocation.
We consider the question of how to best achieve the perception of eye contact when a person is captured by camera and then rendered on a 2D display. For single subjects photographed by a camera, conventional wisdom tells us that looking directly into the camera achieves eye contact. Through empirical user studies, we show that it is instead preferable to {\em look just below the camera lens}. We quantitatively assess where subjects should direct their gaze relative to a camera lens to optimize the perception that they are making eye contact.