Discriminating between neutron and gamma interactions in scintillators is essential for many nuclear science experiments. Pulse-shape discrimination (PSD), based on comparing charge integrations over different regions of a scintillation pulse, is a well-established technique for this purpose. Fully digital PSD data acquisition systems offer high precision and flexibility but generate large data volumes that hinder scalability across thousands of detector channels. Conversely, traditional analog PSD approaches and existing ASIC-based implementations achieve low-latency, high-fidelity processing but rely on bulky, difficult-to-scale readout architectures.

$X$-secure and $T$-private information retrieval (XSTPIR) is a variant of private information retrieval where data security is guaranteed against collusion among up to $X$ servers and the user's retrieval privacy is guaranteed against collusion among up to $T$ servers. Recently, researchers have constructed XSTPIR schemes through the theory of algebraic geometry codes and algebraic curves, with the aim of obtaining XSTPIR schemes that have higher maximum PIR rates for fixed field size and $X,T$ (the number of servers $N$ is not restricted). The mainstream approach is to employ curves of higher genus that have more rational points, evolving from rational curves to elliptic curves to hyperelliptic curves and, most recently, to Hermitian curves. In this paper, we propose a different perspective: with the shared goal of constructing XSTPIR schemes with higher maximum PIR rates, we move beyond the mainstream approach of seeking curves with higher genus and more rational points. Instead, we aim to achieve this goal by enhancing the utilization efficiency of rational points on curves that have already been considered in previous work. By introducing a family of bases for the polynomial space $\text{span}_{\mathbb{F}_q}\{1,x,\dots,x^{k-1}\}$ as an alternative to the Lagrange interpolation basis, we develop two new families of XSTPIR schemes based on rational curves and Hermitian curves, respectively. Parameter comparisons demonstrate that our schemes achieve superior performance. Specifically, our Hermitian-curve-based XSTPIR scheme provides the largest known maximum PIR rates when the field size $q^2\geq 14^2$ and $X+T\geq 4q$. Moreover, for any field size $q^2\geq 28^2$ and $X+T\geq 4$, our two XSTPIR schemes collectively provide the largest known maximum PIR rates.

The I/O cost, defined as the amount of data accessed at helper nodes during the repair process, is a crucial metric for repair efficiency of Reed-Solomon (RS) codes. Recently, a formula that relates the I/O cost to the Hamming weight of some linear spaces was proposed by Liu&Zhang in TCOM-2025. In this work, we introduce an effective method for calculating the Hamming weight of such linear spaces using exponential sums. With this method, we derive lower bounds on the I/O cost for RS codes evaluated on ad-dimensional subspace of Fqℓwithr= 2 or 3 parities.We further design repair schemes for RS codes evaluated on subspaces with any parities. Whenr= 2, ℓ −d+ 1 | ℓ andr= 3,d= ℓ or ℓ−d+2 | ℓ, the I/O cost of our schemes matches the lower bound established in this work. We refer to a scheme that matches the I/O cost lower bound as an I/O-optimal repair scheme. Additionally, forr= 2 withd= ℓ, we fully determine the minimum repair bandwidth of I/O-optimal repair schemes, while forr= 3 withd= ℓ, we construct an I/O-optimal repair scheme achieving a lower repair bandwidth than previous schemes.

Suppose a distributed storage system containingMfiles is replicated acrossNservers, and a user wants to privately retrieve one file by accessing the servers such that the identity of the retrieved file is kept secret from any subset of up toTservers, where each file can be viewed as a vector over theq-ary finite field Fq. A scheme designed for this purpose is called aT-private information retrieval (T-PIR) scheme. We consider the problem of explicitly constructing capacity-achievingT-PIR schemes over small finite fields. In this paper, we first provide a general framework for constructing explicit capacity-achievingT-PIR schemes for all parameters, which only relies on an MDS array matrix with a special information set. To construct such an MDS array matrix, we propose a new family of matrices over finite fields, called the generalized minor matrices of the Moore matrix, and establish a series of key identities. By combining favourable properties of generalized minor matrices with our framework, we construct an explicit capacityachievingT-PIR scheme with optimal sub-packetization over the field Fq, as small as possible, for three classes of parametersN, T,M≥ 3. Specifically, the first class of construction works for allN=d(2t− 1),T=dt, and the field sizeqis the least prime power satisfyingqt−1≥N. Moreover, this construction generalizes the scheme proposed by Xu and Wang in 2022, which only considers the case ofN=d(2t−1),T= dt with 2t−1≥N. For allN=d(2t+ 1),T= dt, our secondT-PIR scheme is the first explicit construction, and the field sizeqis the least prime power satisfyingqt≥N, which is the smallest field size among all known explicit capacity-achievingT-PIR schemes. Particularly, when 2t≥N, the field size of such constructions can be reduced to 2. In the case ofN= 4sandT= 2s+ 1, our scheme is the first one to reduce the field size toq= 2. Compared with all known explicitly capacity-achievingT-PIR schemes, the required field of our schemes has the smallest size.

The deep holes of a linear code are the vectors achieving maximum error distance to the code. There has been a lot of work on the deep holes of Reed -Solomon codes. In this paper, we consider the deep holes of a class of twisted Reed -Solomon codes. The covering radius and a standard class of deep holes of twisted Reed-Solomon codes TRS$k(\mathcal{A},\ \eta)$are obtained for a general evaluation set$\mathcal{A}\subseteq \mathbb{F}_{q}$• Furthermore, when$q=2^{m}\geq 8$, we prove that there are no other deep holes of the full-length twisted Reed-Solomon codes TRS$k(\mathbb{F}_{q},\ \eta)$for$\displaystyle \frac{3}{4}q-1\leq k\leq{q}-4$, and we also completely determine their deep holes for$q-3\leq k\leq q-1$•

Abstract In in‐vehicle driving scenarios, composite action recognition is crucial for improving safety and understanding the driver's intention. Due to spatial constraints and occlusion factors, the driver's range of motion is limited, thus resulting in similar action patterns that are difficult to differentiate. Additionally, collecting skeleton data that characterise the full human posture is difficult, posing additional challenges for action recognition. To address the problems, a novel Graph‐Reinforcement Transformer (GR‐Former) model is proposed. Using limited skeleton data as inputs, by introducing graph structure information to directionally reinforce the effect of the self‐attention mechanism, dynamically learning and aggregating features between joints at multiple levels, the authors’ model constructs a richer feature vector space, enhancing its expressiveness and recognition accuracy. Based on the Drive & Act dataset for composite action recognition, the authors’ work only applies human upper‐body skeleton data to achieve state‐of‐the‐art performance compared to existing methods. Using complete human skeleton data also has excellent recognition accuracy on the NTU RGB + D‐ and NTU RGB + D 120 dataset, demonstrating the great generalisability of the GR‐Former. Generally, the authors’ work provides a new and effective solution for driver action recognition in in‐vehicle scenarios.

In distributed storage, cooperative repair is to simultaneously recoverh(h> 1) node erasures by downloading data from surviving nodes as well as collaboration between thehreplacement nodes. In this work, we propose a generalized cooperative repair framework for Reed-Solomon (RS) codes with two erasures. The key idea is to construct parity-check polynomials for the two replacement nodes respectively and then reduce the repair problem to the design of a linearized permutation polynomial related to the parity-check polynomials. We provide constructions of the linearized permutation polynomial in several cases, leading to cooperative repair schemes accordingly. Compared with the schemes given by Dauet al. 2021, our schemes retain the same repair bandwidth while apply to a much wider parameter regime and need only one-round collaboration. Finally we further reduce the repair bandwidth by the lifting method for RS codes of short length.

In this paper, due to the important value in practical applications, we consider the coded distributed matrix multiplication problem of computing$AA^{\top} $in a distributed computing system with$N$worker nodes and a master node, where the input matrices$A$and$A^{\top} $are partitioned into$m$-by-$p$and$p$-by-$m$blocks of equal-size sub-matrices respectively. For effective straggler mitigation, we propose a novel computation strategy, named folded polynomial code, which is obtained by modifying the entangled polynomial codes. Moreover, we characterize a lower bound on the optimal recovery threshold among all linear computation strategies when the underlying field is the real number field, and our folded polynomial codes can achieve this bound in the case of$m=1$. Compared with all known computation strategies for coded distributed matrix multiplication, our folded polynomial codes outperform them in terms of recovery threshold, download cost, and decoding complexity.

The$T$-Private Information Retrieval ($T$-PIR) problem is that a user wishes to retrieve a single record from$N$servers, without revealing the identity of the desired record even if the number of colluding servers up to$T$. Here every server stores all$M$records and each record can be viewed as a vector over the$q$-ary finite field$\mathbb {F}_{q}$. To reduce the field size, a capacity-achieving$T$-PIR scheme based on some MDS array codes for all possible$N>T,M\geq 2$was constructed by Xu and Zhang in 2019. A key idea in that scheme is to construct some MDS array codes in query phase, whose generator matrices satisfy the recovery property (see (C1) inExample 1, page 6),i.e.,there exist some specific columns in each generator matrix such that the number of them is equal to the rank of such matrix. We call the set of each column index of those columns in each generator matrix as the column index set. However, that scheme didn’t give an explicit selection of the column index set satisfying the recovery property. In this paper, let$N=d(2t-1)$,$N>T=dt>1, M\geq 3$and$d\geq 1$, under the constraint of$2^{t-1}\geq N$, we present a novel method to construct capacity-achieving$T$-PIR schemes over the binary field with an explicit selection of the column index set. Moreover, our scheme has sub-packetization$N(2t-1)^{M-2}$, which is optimal for all linear capacity-achieving$T$-PIR schemes determined by Zhang and Xu in 2019. The key to our method is that all locators and column multipliers are precisely selected such that a Generalized Reed-Solomon (GRS) code defined by them has a zero-dimensional subfield sub-code. Compared with all the known capacity-achieving$T$-PIR schemes for the same non-trivial parameters, ours is the first explicit capacity-achieving$T$-PIR scheme over the binary field.

Suppose a database containing M records is replicated in each of N servers, and a user wants to privately retrieve one record by accessing the servers such that identity of the retrieved record is secret against any up to T servers. A scheme designed for this purpose is called a T -private information retrieval (T -PIR) scheme.In this paper we focus on the field size of T -PIR schemes. We design a general capacity-achieving T -PIR scheme whose queries are generated by using some MDS array codes. It only requires field size q≥ℓ√N, where ℓ = min {tM-2, (n - t)M-2}, t = T/gcd(N, T), n = N/gcd(N, T) and has the optimal sub-packetization NnM-2. Comparing with existing capacity-achieving T -PIR schemes, our scheme has the following advantage, that is, its field size monotonically decreases as the number of records M grows. In particular, the binary field is sufficient for building a capacity-achieving T-PIR scheme as long as M ≥ 2 + ⌈logμlog2N⌉, where μ = min{t, n - t} > 1.

Suppose M records are replicated in N servers (each storing all M records), a user wants to privately retrieve one record by accessing the servers such that the identity of the retrieved record is secret against any up to T servers. A scheme designed for this purpose is called a T-private information retrieval (PIR) scheme. In practice, capacity-achieving and small sub-packetization are both desired for PIR schemes, because the former implies the highest download rate and the latter means simple realization. Meanwhile, sub-packetization is the key technique for achieving capacity. In this paper, we characterize the optimal sub-packetization for linear capacity-achieving T-PIR schemes. First, a lower bound on the sub-packetization L for linear capacity-achieving T-PIR schemes is proved, i.e., L ≥ dnM-1, where d = gcd(N, T) and n = N/d. Then, for general values of M and N > T ≥ 1, a linear capacity-achieving T-PIR scheme with sub-packetization dnM-1is designed. Comparing with the first capacity-achieving T-PIR scheme given by Sun and Jafar in 2016, our scheme reduces the sub-packetization from NMto the optimal and further reduces the field size by a factor of NdM-2.

Consider N servers with replicated databases containing M records. Suppose a user wants to privately retrieve one record by accessing the servers such that the identity of the retrieved record is secret against any up to T servers. A scheme designed for this purpose is called a T -private information retrieval ( T -PIR) scheme. Three indexes are concerned for PIR schemes: (1) rate, indicating the amount of retrieved information per unit of downloaded data. The highest achievable rate is characterized by the capacity; (2) sub-packetization, reflecting the implementation complexity for linear schemes; (3) field size. We consider linear schemes over a finite field. In this paper, a general T - PIR scheme simultaneously attaining the optimality of almost all of the three indexes is presented. Specifically, we design a linear capacity-achieving T-PIR scheme with sub-packetization dnM-1over a finite field \mathbbFq, q ≥ N. The sub-packetization dnM-1, where d=gcd(N, T) and n=N/d, has been proved to be optimal in our previous work. The field size is reduced by an exponential factor in our scheme comparing with existing capacity -achieving T - PIR schemes.

The influence of spatial position means how deep it affects the spatial objects and can be measured by the number of affected spatial objects. The evaluation of spatial position influence which widely used in architectural planning and facility location is a typical study in the spatial database. In previous studies, a spatial object was supposed to affect only one spatial position, the influence of the object calculated by the number of the space objects in the area. However, the spatial object can affect many spatial positions and the effects are multiple. In this study, we provide a new evaluation model based on RkNN. A new measurement method was proposed by calculating the weight of the contribution based on the distance between the space object and the space position. The new measurement method makes the model more suitable for the practical application. In addition, a location algorithm was proposed based on the RkNN influence evaluation model. The algorithm can solve the problem such as making the facilities to provide the best service to the customers and using each facility effectively. The influence of each facility is calculated in this algorithm and the rationality of the location scheme is evaluated by equilibrium coefficient, the smaller the equilibrium coefficient, the more reasonable the scheme. The location algorithm based on the new model shows a better performance in the practical application, it contributes to the more reasonable and effective facility location.