arXiv subjects
Publications and source records attributed to Cong Ding.
Let $G/P$ be a complex projective rational homogeneous variety of dimension $2m+1$. We prove that $G/P$ is an equivariant compactification of the Heisenberg group of dimension $2m+1$ if and only if it is isomorphic to either an adjoint variety, or the 3-dimensional smooth quadric $Q^3$, or a product $\mathbb{P}^{2m+1-d} \times Y$ with $1 \leq d=\dim Y \leq m$, where $Y$ is a product of cominuscule varieties.
A Schubert variety $X_0$ on a rational homogenous space $X=G/P$ is said to be homologically rigid, if any subvariety $Z$ on $X$ representing the same homology class with $X_0$ must satisfy $Z=g\cdot X_0$ for some $g\in{\rm Aut_0}(X)$. We say $X_0$ is Schur rigid, if furthermore any subvariety $Z$ on $X$ whose homology class is a multiple $r$ of that of $X_0$ must satisfy $Z=g_1\cdot X_0+\cdots+g_r\cdot X_0$ for some $g_1,\cdots ,g_r\in{\rm Aut_0}(X)$. Homological rigidity and Schur rigidity of Schubert varieties in rational homogeneous spaces of Picard number one have been well studied in extensive literature. In this paper, we study both rigidity problems of Schubert varieties in rational homogeneous spaces of higher Picard numbers. We show that in the long root cases, including all cases when $G$ is of type $ADE$, smooth Schubert varieties have homological rigidity. Besides, we give the complete list of Schubert varieties of subdiagram type with/without homological rigidity. Furthermore, for a Schubert variety $X_0$ of subdiagram type, we show that it has Schur rigidity in long root cases unless $X_0$ admits a fiber bundle structure over the projective space.
We prove that the Heisenberg group $\h_{2n+1}$ admits infinitely many inequivalent equivariant compactifications into $\mathbb{P}^{2n+1}$ for all $n\geq 1$. This result provides an analog of Hassett-Tschinkel's classical result beyond commutative algebraic groups.
To address the challenge of extending the transmission range of implantable TXs while also minimizing their size and power consumption, this paper introduces a transcutaneous, high data-rate, fully integrated IR-UWB transmitter that employs a novel co-designed power amplifier (PA) and antenna interface for enhanced performance. With the co-designed interface, we achieved the smallest footprint of 49.8mm2 and the longest transmission range of 1.5m compared to the state-of-the-art IR-UWB TXs.
We classify smooth Euler-symmetric varieties corresponding to the symbol system generated by a single reduced polynomial.
In multistate non-Hermitian systems, higher-order exceptional points and exotic phenomena with no analogues in two-level systems arise. A paradigm is the exceptional nexus (EX), a third-order EP as the cusp singularity of exceptional arcs (EAs), that has a hybrid topological nature. Using atomic Bose-Einstein condensates to implement a dissipative three-state system, we experimentally realize an EX within a two-parameter space, despite the absence of symmetry. The engineered dissipation exhibits density dependence due to the collective atomic response to resonant light. Based on extensive analysis of the system's decay dynamics, we demonstrate the formation of an EX from the coalescence of two EAs with distinct geometries. These structures arise from the different roles played by dissipation in the strong coupling limit and quantum Zeno regime. Our work paves the way for exploring higher-order exceptional physics in the many-body setting of ultracold atoms.
The notion of admissible pairs of rational homogeneous spaces of Picard number one and their rigidity in terms of the geometric substructures was formulated by Mok and Zhang. The rigidity is known for subdiagram type. While when the admissible pair is of deletion type, the rigidity no longer holds and we need additional conditions. Mok gave a general criterion to handle the admissible pairs which are not of subdiagram type. In this short note we give some examples of admissible pairs of irreducible compact Hermitian symmetric spaces of deletion type to be rigid under the assumption of rational saturation, as an application of Mok's theorem.
We construct a sequence of explicit blow-ups and blow-downs on irreducible compact Hermitian symmetric spaces $X$ which transforms it into a projective space of the same dimension. Moreover this resolves a birational map given by Landsberg and Manivel. Centers of the blow-ups for $X$ are constructed by loci of chains of minimal rational curves and centers of the blow-ups for the projective space are constructed from the variety of minimal rational tangents of $X$ and its higher secant varieties.
Most existing person re-identification methods compute the matching relations between person images across camera views based on the ranking of the pairwise similarities. This matching strategy with the lack of the global viewpoint and the context's consideration inevitably leads to ambiguous matching results and sub-optimal performance. Based on a natural assumption that images belonging to the same person identity should not match with images belonging to multiple different person identities across views, called the unicity of person matching on the identity level, we propose an end-to-end person unicity matching architecture for learning and refining the person matching relations. First, we adopt the image samples' contextual information in feature space to generate the initial soft matching results by using graph neural networks. Secondly, we utilize the samples' global context relationship to refine the soft matching results and reach the matching unicity through bipartite graph matching. Given full consideration to real-world person re-identification applications, we achieve the unicity matching in both one-shot and multi-shot settings of person re-identification and further develop a fast version of the unicity matching without losing the performance. The proposed method is evaluated on five public benchmarks, including four multi-shot datasets MSMT17, DukeMTMC, Market1501, CUHK03, and a one-shot dataset VIPeR. Experimental results show the superiority of the proposed method on performance and efficiency.
Growing evidence suggests that phase-locked deep brain stimulation (DBS) can effectively regulate abnormal brain connectivity in neurological and psychiatric disorders. This letter therefore presents a low-power SoC with both neural connectivity extraction and phase-locked DBS capabilities. A 16-channel low-noise analog front-end (AFE) records local field potentials (LFPs) from multiple brain regions with precise gain matching. A novel low-complexity phase estimator and neural connectivity processor subsequently enable energy-efficient, yet accurate measurement of the instantaneous phase and cross-regional synchrony measures. Through flexible combination of neural biomarkers such as phase synchrony and spectral energy, a four-channel charge-balanced neurostimulator is triggered to treat various pathological brain conditions. Fabricated in 65nm CMOS, the SoC occupies a silicon area of 2.24mm2 and consumes 60uW, achieving over 60% power saving in neural connectivity extraction compared to the state-of-the-art. Extensive in-vivo measurements demonstrate multi-channel LFP recording, real-time extraction of phase and neural connectivity measures, and phase-locked stimulation in rats.
Closed-loop neural interfaces with on-chip machine learning can detect and suppress disease symptoms in neurological disorders or restore lost functions in paralyzed patients. While high-density neural recording can provide rich neural activity information for accurate disease-state detection, existing systems have low channel counts and poor scalability, which could limit their therapeutic efficacy. This work presents a highly scalable and versatile closed-loop neural interface SoC that can overcome these limitations. A 256-channel time-division multiplexed (TDM) front-end with a two-step fast-settling mixed-signal DC servo loop (DSL) is proposed to record high-spatial-resolution neural activity and perform channel-selective brain-state inference. A tree-structured neural network (NeuralTree) classification processor extracts a rich set of neural biomarkers in a patient- and disease-specific manner. Trained with an energy-aware learning algorithm, the NeuralTree classifier detects the symptoms of underlying disorders (e.g., epilepsy and movement disorders) at an optimal energy-accuracy tradeoff. A 16-channel high-voltage (HV) compliant neurostimulator closes the therapeutic loop by delivering charge-balanced biphasic current pulses to the brain. The proposed SoC was fabricated in 65-nm CMOS and achieved a 0.227-$\mu$J/class energy efficiency in a compact area of 0.014mm$^2$/channel. The SoC was extensively verified on human electroencephalography (EEG) and intracranial EEG (iEEG) epilepsy datasets, obtaining 95.6%/94% sensitivity and 96.8%/96.9% specificity, respectively. In vivo neural recordings using soft $\mu$ECoG arrays and multi-domain biomarker extraction were further performed on a rat model of epilepsy. In addition, for the first time in literature, on-chip classification of rest-state tremor in Parkinson's disease (PD) from human local field potentials (LFPs) was demonstrated.
Tuning a database system to achieve optimal performance on a given workload is a long-standing problem in the database community. A number of recent works have leveraged ML-based approaches to guide the sampling of large parameter spaces (hundreds of tuning knobs) in search for high performance configurations. Looking at Microsoft production services operating millions of databases, sample efficiency emerged as a crucial requirement to use tuners on diverse workloads. This motivates our investigation in LlamaTune, a tuner design that leverages domain knowledge to improve the sample efficiency of existing optimizers. LlamaTune employs an automated dimensionality reduction technique based on randomized projections, a biased-sampling approach to handle special values for certain knobs, and knob values bucketization, to reduce the size of the search space. LlamaTune compares favorably with the state-of-the-art optimizers across a diverse set of workloads. It identifies the best performing configurations with up to $11\times$ fewer workload runs, and reaching up to $21\%$ higher throughput. We also show that benefits from LlamaTune generalize across both BO-based and RL-based optimizers, as well as different DBMS versions. While the journey to perform database tuning at cloud-scale remains long, LlamaTune goes a long way in making automatic DBMS tuning practical at scale.
Data loading has been one of the most common performance bottlenecks for many big data applications, especially when they are running on inefficient human-readable formats, such as JSON or CSV. Parsing, validating, integrity checking and data structure maintenance are all computationally expensive steps in loading these formats. Regardless of these costs, many records may be filtered later during query evaluation due to highly selective predicates -- resulting in wasted computation. Meanwhile, the computing power of client ends is typically not exploited. Here, we explore investing limited cycles of clients on prefiltering to accelerate data loading and enable data skipping for query execution. In this paper, we present CIAO, a tunable system to enable client cooperation with the server to enable efficient partial loading and data skipping for a given workload. We proposed an efficient algorithm that would select a near-optimal predicate set to push down within a given budget. Moreover, CIAO will address the trade-off between client cost and server savings by setting different budgets for different clients. We implemented CIAO and evaluated its performance on three real-world datasets. Our experimental results show that the system substantially accelerates data loading by up to 21x and query execution by up to 23x and improves end-to-end performance by up to 19x within a budget of 1.0 microseconds latency per record on clients.
Let $M$ be a complex manifold. We prove that a compact submanifold $S\subset M$ with splitting tangent sequence (called a splitting submanifold) is rational homogeneous when $M$ is in a large class of rational homogeneous spaces of Picard number one. Moreover, when $M$ is irreducible Hermitian symmetric, we prove that $S$ must be also Hermitian symmetric. The basic tool we use is the restriction and projection map $\pi$ of the global holomorphic vector fields on the ambient space which is induced from the splitting condition. The usage of global holomorphic vector fields may help us set up a new scheme to classify the splitting submanifolds in explicit examples, as an example we give a differential geometric proof for the classification of compact splitting submanifolds with $\dim\geq 2$ in a hyperquadric, which has been previously proven using algebraic geometry.
We prove a gap rigidity theorem for diagonal curves in irreducible compact Hermitian symmetric spaces of tube type, which is a dual analogy to a theorem obtained by Mok in noncompact case. Motivated by the proof we give a theorem on weaker gap rigidity problems for higher dimensional submanifolds.