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Tao Feng

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Published work

45 published item(s)

preprint2026arXiv

RouteProfile: Elucidating the Design Space of LLM Profiles for Routing

As the large language model (LLM) ecosystem expands, individual models exhibit varying capabilities across queries, benchmarks, and domains, motivating the development of LLM routing. While prior work has largely focused on router mechanism design, LLM profiles, which capture model capabilities, remain underexplored. In this work, we ask: How does LLM profile design affect routing performance across different routers? Addressing this question helps clarify the role of profiles in routing, disentangle profile design from router design, and enable fairer comparison and more principled development of routing systems. To this end, we view LLM profiling as a structured information integration problem over heterogeneous interaction histories. We develop a general design space of LLM profiles, named RouteProfile, along four key dimensions: organizational form, representation type, aggregation depth, and learning configuration. Through systematic evaluation across three representative routers under both standard and new-LLM generalization settings, we show that: (1) structured profiles consistently outperform flat ones; (2) query-level signals are more reliable than coarse domain-level signals; and (3) generalization to newly introduced models benefits most from structured profiles under trainable configurations. Overall, our work highlights LLM profile design as an important direction for future routing research.

preprint2022arXiv

Giant transverse and longitudinal magneto-thermoelectric effect in polycrystalline nodal-line semimetal Mg3Bi2

Topological semimetals provide new opportunities for exploring new thermoelectric phenomena, because of their exotic and nontrivial electronic structure topology around the Fermi surface. In this study, we report on the discovery of giant transverse and longitudinal magneto-thermoelectric (MTE) effects in Mg3Bi2, which is predicted to be a type-II nodal-line semimetal in the absence of spin-orbit coupling (SOC). The maximum transverse power factor is 2182 μWm^{-1}K^{-2} at 13.5 K and 6 Tesla. The longitudinal power factor reaches up to 3043μWm^{-1}K^{-2} at 15 K and 13 Tesla, which is 20 times higher than in a zero-strength magnetic field and is also comparable to state-of-the-art MTE materials. By compensating Mg loss in the Mg-rich conditions for turning carrier concentration, the sample obtained in this work shows a large linear non-saturating magnetoresistance of 940% under a field of 14 Tesla. This is a two-orders-of-magnitude increase with respect to the normal Mg-deficiency Mg3Bi2 sample. Using density functional calculations, we attribute the underlying mechanism to the parent nodal-line electronic structure without SOC and the anisotropic Fermi surface shape with SOC, highlighting the essential role of high carrier mobility and open electron orbits in moment space. Our work offers a new avenue toward highly efficient thermoelectric materials through the design of Fermi surfaces with special topological electronic structures in novel quantum materials.

preprint2022arXiv

Linear codes associated with the Desarguesian ovoids in $Q^+(7,q)$

The Desarguesian ovoids in the orthogonal polar space $Q^+(7,q)$ with $q$ even have first been introduced by Kantor by examining the $8$-dimensional absolutely irreducible modular representations of $\text{PGL}(2,q^3)$. We investigate this module for all prime power values of $q$. The shortest $\text{PGL}(2,q^3)$-orbit $O$ gives the Desarguesian ovoid in $Q^+(7,q)$ for even $q$ and it is known to give a complete partial ovoid of the symplectic polar space $W(7,q)$ for odd~$q$. We determine the hyperplane sections of $O$. As a corollary, we obtain the parameters $[q^3+1,8,q^3-q^2-q]_q$ and the weight distribution of the associated $\mathbb{F}_q$-linear code $C_O$ and the parameters $[q^3+1,q^3-7,5]_q$ of the dual code $C_O^\perp$ for $q \ge 4$. We also show that both codes $C_O$ and $C_O^\perp$ are length-optimal for all prime power values of $q$.

preprint2022arXiv

Overcoming Catastrophic Forgetting in Incremental Object Detection via Elastic Response Distillation

Traditional object detectors are ill-equipped for incremental learning. However, fine-tuning directly on a well-trained detection model with only new data will lead to catastrophic forgetting. Knowledge distillation is a flexible way to mitigate catastrophic forgetting. In Incremental Object Detection (IOD), previous work mainly focuses on distilling for the combination of features and responses. However, they under-explore the information that contains in responses. In this paper, we propose a response-based incremental distillation method, dubbed Elastic Response Distillation (ERD), which focuses on elastically learning responses from the classification head and the regression head. Firstly, our method transfers category knowledge while equipping student detector with the ability to retain localization information during incremental learning. In addition, we further evaluate the quality of all locations and provide valuable responses by the Elastic Response Selection (ERS) strategy. Finally, we elucidate that the knowledge from different responses should be assigned with different importance during incremental distillation. Extensive experiments conducted on MS COCO demonstrate our method achieves state-of-the-art result, which substantially narrows the performance gap towards full training.

preprint2022arXiv

Platooning of Connected Vehicles with Directed Graph: $H_\infty$ Robustness Analysis and Synthesis

This paper revisits the robustness analysis and distributed ${ H}_\infty$ controller design for the platooning of connected vehicles. Recently, the relevant result subjected to the undirected topology has been studied, in the light of the symmetry of Laplace matrix. It is well known that the same problem is more challenging for the \emph{directed} topology, since the Laplace matrix ceases to be symmetric. In this paper, the problem is solved by introducing more weighting parameters and setting suitable values for them. Then we show that the introduced weighting parameters lead to a positive effect on robustness, and solve the problem of feedback high gain. Finally, two numerical simulations and a practical simulation based on Next Generation Simulation (NGSIM) dataset are used to illustrate the effectiveness of our method.

preprint2021arXiv

A construction of minimal linear codes from partial difference sets

In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a minimal linear code by a character-theoretical approach. We obtain new three-weight or four-weight minimal linear codes that do not satisfy the Ashikhmin-Barg condition by using partial difference sets. We show that our construction yields minimal linear codes that do not arise from cutting vectorial blocking sets, and also discuss their applications in secret sharing schemes.

preprint2021arXiv

Coupling effect and pole assignment in trajectory regulation of multi-agent systems

This paper revisits a well studied leader-following consensus problem of linear multi-agent systems, while aiming at follower nodes' transient performance. Conventionally, when not all follower nodes have access to the leader's state information, distributed observers are designed to estimate the leader's state, and the observers are coupled via communication network. Then each follower node only needs to track its observer's state independently, without interacting with its neighbors. This paper deliberately introduces certain coupling effect among follower nodes, such that the follower nodes tend to converge to each other cooperatively on the way they converge to the leader. Moreover, by suitably designing the control law, the poles of follower nodes can be assigned as desired, and thus transient tracking performance can also be adjusted.

preprint2021arXiv

Reinforced Contact Tracing and Epidemic Intervention

The recent outbreak of COVID-19 poses a serious threat to people's lives. Epidemic control strategies have also caused damage to the economy by cutting off humans' daily commute. In this paper, we develop an Individual-based Reinforcement Learning Epidemic Control Agent (IDRLECA) to search for smart epidemic control strategies that can simultaneously minimize infections and the cost of mobility intervention. IDRLECA first hires an infection probability model to calculate the current infection probability of each individual. Then, the infection probabilities together with individuals' health status and movement information are fed to a novel GNN to estimate the spread of the virus through human contacts. The estimated risks are used to further support an RL agent to select individual-level epidemic-control actions. The training of IDRLECA is guided by a specially designed reward function considering both the cost of mobility intervention and the effectiveness of epidemic control. Moreover, we design a constraint for control-action selection that eases its difficulty and further improve exploring efficiency. Extensive experimental results demonstrate that IDRLECA can suppress infections at a very low level and retain more than 95% of human mobility.

preprint2020arXiv

Time of arrival imaging: The proof of concept for a novel medical imaging modality

It has been shown that with the use of ultra-wideband (UWB) electromagnetic signal and time of arrival (ToA) principle, it is possible to locate medical implants given the permittivity distribution of the body. We propose a new imaging modality using the reverse process to acquire permittivity distributions as a surrogate of human anatomy. In the proposed systems, the locations of the signal source, receiver, and signal shapes are assumed to be known exactly. The measured data is recorded as the time it takes for the signal to travel from the signal source to the signal receiver. The finite-difference-time-domain (FDTD) method is used for the modeling of signal propagation within the phantom, which is used for both simulation and image reconstruction. Image reconstruction is achieved using linear regression on the training pairs, which includes randomly generated images and its corresponding arrival times generated using the FDTD approach. The linear weights of the training images are generated to minimize the difference between the arrival time of the reconstruction image and the measured arrival time. A simulation study using UWB signal with the central frequency of 300 MHz and the Shepp-Logan phantom was carried out. Ten-picosecond timing resolution is used for the simulation and image reconstruction. The quantitative difference between the arrival times of the phantom and the reconstructed image reduced with an increased iteration number. The quantitative error of the reconstructed image reached below 10% after 900 iterations, and 8.4% after 1200 iterations. With additional post-smoothing to suppress the introduced noise pattern through reconstruction, 6.5% error was achieved. In this paper, an approach that utilizes the ToA principle to achieve transmission imaging with radio waves is proposed and validated using a simulation study.

preprint2016arXiv

Some new results on permutation polynomials over finite fields

Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, four classes of monomial complete permutation polynomials and one class of trinomial complete permutation polynomials are presented, one of which confirms a conjecture proposed by Wu et al. (Sci. China Math., to appear. Doi: 10.1007/s11425-014-4964-2). Furthermore, we give two classes of trinomial permutation polynomials, and make some progress on a conjecture about the differential uniformity of power permutation polynomials proposed by Blondeau et al. (Int. J. Inf. Coding Theory, 2010, 1, pp. 149-170).

preprint2015arXiv

A family of $m$-ovoids of parabolic quadrics

We construct a family of $\frac{(q-1)}{2}$-ovoids of $Q(4,q)$, the parabolic quadric of $\textup{PG}(4,q)$, for $q\equiv 3\pmod 4$. The existence of $\frac{(q-1)}{2}$-ovoids of $Q(4,q)$ was only known for $q=3, 7,$ or $11$. Our construction provides the first infinite family of $\frac{(q-1)}{2}$-ovoids of $Q(4,q)$.Along the way, we also give a construction of $\frac{q+1}{2}$-ovoids in $Q(4,q)$ for $q\equiv 1\pmod 4$.

preprint2015arXiv

Cameron-Liebler line classes with parameter $x=\frac{q^2-1}{2}$

In this paper, we give an algebraic construction of a new infinite family of Cameron-Liebler line classes with parameter $x=\frac{q^2-1}{2}$ for $q\equiv 5$ or $9\pmod{12}$, which generalizes the examples found by Rodgers in \cite{rodgers} through a computer search. Furthermore, in the case where $q$ is an even power of $3$, we construct the first infinite family of affine two-intersection sets in $\mathrm{AG}(2,q)$.

preprint2015arXiv

Three-valued Gauss periods, circulant weighing matrices and association schemes

Gauss periods taking exactly two values are closely related to two-weight irreducible cyclic codes and strongly regular Cayley graphs. They have been extensively studied in the work of Schmidt and White and others. In this paper, we consider the question of when Gauss periods take exactly three rational values. We obtain numerical necessary conditions for Gauss periods to take exactly three rational values. We show that in certain cases, the necessary conditions obtained are also sufficient. We give numerous examples where the Gauss periods take exactly three vlaues. Furthermore, we discuss connections between three-valued Gauss periods and combinatorial structures such as circulant weighing matrices and 3-class association schemes.

preprint2014arXiv

Design of an Encryption-Decryption Module Oriented for Internet Information Security SOC Design

In order to protect the security of network data, a high speed chip module for encrypting and decrypting of network data packet is designed. The chip module is oriented for internet information security SOC (System on Chip) design. During the design process, AES (Advanced Encryption Standard) and 3DES (Data Encryption Standard) encryption algorithm are adopted to protect the security of network data. The following points are focused: (1) The SOC (System on Chip) design methodology based on IP (Intellectual Property) core is used. AES (Advanced Encryption Standard) and 3DES (Data Encryption Standard) IP (Intellectual Property) cores are embedded in the chip module, peripheral control sub-modules are designed to control the encryption-decryption module, which is capable of shortening the design period of the chip module. (2) The implementation of encryption-decryption with hardware was presented, which improves the safety of data through the encryption-decryption chip and reduce the load of CPU. (3) In our hardware solution, two AES (Advanced Encryption Standard) cores are used to work in parallel, which improves the speed of the encryption module. Moreover, the key length of AES (Advanced Encryption Standard) encryption algorithm is designed with three optional configurations at 128 bits, 256 bits and 192 bits respectively and six optional encryption algorithm modes: CBC (Cipher Block Chaining) mode, ECB (Electronic Code Book) mode, GCM (Galois/Counter Mode) mode, XTS(cipherteXT Stealing) mode, CTR (CounTeR) mode and 3DES respectively, which adds the flexibility to its applications.

preprint2014arXiv

Key parameters generation of the navigation data of GPS Simulator

The development of the GPS (Global Positioning System) signal simulator involving to a number of key technologies, in which the generation of navigation message has important significance. Based on analysis of the structure of GPS navigation data, the paper researches the production of telemetry word and handover word, parity check code, time parameters and star clock. Using disturbing force equation and Lagrange planetary motion equation extrapolate ephemeris parameters whose feasibility is verified through the Matlab software finally.

preprint2014arXiv

New pseudo-planar binomials in characteristic two and related schemes

Planar functions in odd characteristic were introduced by Dembowski and Ostrom in order to construct finite projective planes in 1968. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and signal sets. Recently, a new notion of pseudo-planar functions in even characteristic was proposed by Zhou. These new pseudo-planar functions, as an analogue of planar functions in odd characteristic, also bring about finite projective planes. There are three known infinite families of pseudo-planar monomial functions constructed by Schmidt and Zhou, and Scherr and Zieve. In this paper, three new classes of pseudo-planar binomials are provided. Moreover, we find that each pseudo-planar function gives an association scheme which is defined on a Galois ring.

preprint2014arXiv

On the Existence of Certain Optimal Self-Dual Codes with Lengths Between $74$ and $116$

The existence of optimal binary self-dual codes is a long-standing research problem. In this paper, we present some results concerning the decomposition of binary self-dual codes with a dihedral automorphism group $D_{2p}$, where $p$ is a prime. These results are applied to construct new self-dual codes with length $78$ or $116$. We obtain $16$ inequivalent self-dual $[78,39,14]$ codes, four of which have new weight enumerators. We also show that there are at least $141$ inequivalent self-dual $[116,58,18]$ codes, most of which are new up to equivalence. Meanwhile, we give some restrictions on the weight enumerators of singly even self-dual codes. We use these restrictions to exclude some possible weight enumerators of self-dual codes with lengths $74$, $76$, $82$, $98$ and $100$.

preprint2014arXiv

On the Weight Distribution of Cyclic Codes with Niho Exponents

Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. More specifically, we obtain two classes of binary three-weight and four-weight cyclic codes and a class of nonbinary four-weight cyclic codes. The weight distributions follow from the determination of value distributions of certain exponential sums. Several examples are presented to show that some of our codes are optimal and some have the best known parameters.

preprint2014arXiv

Semi-cyclic holey group divisible designs with block size three and applications to sampling designs and optical orthogonal codes

We consider the existence problem for a semi-cyclic holey group divisible design of type (n,m^t) with block size 3, which is denoted by a 3-SCHGDD of type (n,m^t). When t is odd and n\neq 8 or t is doubly even and t\neq 8, the existence problem is completely solved; when t is singly even, many infinite families are obtained. Applications of our results to two-dimensional balanced sampling plans and optimal two-dimensional optical orthogonal codes are also discussed.

preprint2014arXiv

Two-dimensional balanced sampling plans avoiding adjacent units

Hedayat et al. first introduced balanced sampling plans for the exclusion of contiguous units. Wright detailed the results of a preliminary investigation of two-dimensional balanced sampling plans avoiding adjacent units (2-BSAs), and pointed out explicitly three types of 2-BSAs, which have different adjacency scheme, namely "Row and Column", "Sharing a Border" and "Island". This paper will provide more details for the three types of 2-BSAs from the point of view of design theory.

preprint2013arXiv

Combinatorial constructions for optimal two-dimensional optical orthogonal codes with $λ$ = 2

In this paper, we are concerned about optimal two-dimensional optical orthogonal codes with $λ$ = 2. Some combinatorial constructions are presented and many infinite families of optimal two-dimensional optical orthogonal codes with weight 4 and $λ$ = 2 are obtained. Especially, we shall see that in many cases an optimal two-dimensional optical orthogonal code can not achieve the Johnson bound.

preprint2013arXiv

Difference Sets with Few Character Values

The known families of difference sets can be subdivided into three classes: difference sets with Singer parameters, cyclotomic difference sets, and difference sets with gcd$(v,n)>1$. It is remarkable that all the known difference sets with gcd$(v,n)>1$ have the so-called character divisibility property. In 1997, Jungnickel and Schmidt posed the problem of constructing difference sets with gcd$(v,n)>1$ that do not satisfy this property. In an attempt to attack this problem, we use difference sets with three nontrivial character values as candidates, and get some necessary conditions.

preprint2013arXiv

Nonsymmetric primitive translation schemes on prime power number of vertices

It is well-known that translation schemes on prime number of vertices are exactly the cyclotomic schemes. In this current paper, we show that there are no nonsymmetric primitive translation schemes on prime square vertices with at most four classes. On the other hand, we find new non-symmetric four- and five-class association schemes from cyclotomy as fission schemes of certain symmetric three-class schemes. Moreover, we provide an affirmative answer to the following question raised by Song \cite{song_2}: Are there any other two-class primitive schemes that admit symmetrizable fission schemes besides the cyclotomic scheme of index 2 for $q \equiv5 \pmod{8}$? To be more specific, we show that a certain two-class primitive scheme in the finite field $\F_{37^3}$ constructed by Feng and Xiang in \cite{fx} admits a four-class fission scheme. This fission scheme is realized as a fusion scheme of the cyclotomic scheme of index 28.

preprint2013arXiv

Quantum channels from association schemes

We propose in this note the study of quantum channels from association schemes. This is done by interpreting the $(0,1)$-matrices of a scheme as the Kraus operators of a channel. Working in the framework of one-shot zero-error information theory, we give bounds and closed formulas for various independence numbers of the relative non-commutative (confusability) graphs, or, equivalently, graphical operator systems. We use pseudocyclic association schemes as an example. In this case, we show that the unitary entanglement-assisted independence number grows at least quadratically faster, with respect to matrix size, than the independence number. The latter parameter was introduced by Beigi and Shor as a generalization of the one-shot Shannon capacity, in analogy with the corresponding graph-theoretic notion.

preprint2013arXiv

Semi-cyclic holey group divisible designs with block size three

In this paper we discuss the existence problem for a semi-cyclic holey group divisible design of type (n,m^t) with block size 3, which is denoted by a 3-SCHGDD of type (n,m^t). When n=3, a 3-SCHGDD of type (3,m^t) is equivalent to a (3,mt;m)-cyclic holey difference matrix, denoted by a (3,mt;m)-CHDM. It is shown that there is a (3,mt;m)-CHDM if and only if (t-1)m\equiv 0 (mod 2) and t\geq 3 with the exception of m\equiv 0 (mod 2) and t=3. When n\geq 4, the case of t odd is considered. It is established that if t\equiv 1 (mod 2) and n\geq 4, then there exists a 3-SCHGDD of type (n,m^t) if and only if t\geq 3 and (t-1)n(n-1)m\equiv 0 (mod 6) with some possible exceptions of n=6 and 8. The main results in this paper have been used to construct optimal two-dimensional optical orthogonal codes with weight 3 and different auto- and cross-correlation constraints by the authors recently.

preprint2013arXiv

Some New Results on the Cross Correlation of $m$-sequences

The determination of the cross correlation between an $m$-sequence and its decimated sequence has been a long-standing research problem. Considering a ternary $m$-sequence of period $3^{3r}-1$, we determine the cross correlation distribution for decimations $d=3^{r}+2$ and $d=3^{2r}+2$, where $\gcd(r,3)=1$. Meanwhile, for a binary $m$-sequence of period $2^{2lm}-1$, we make an initial investigation for the decimation $d=\frac{2^{2lm}-1}{2^{m}+1}+2^{s}$, where $l \ge 2$ is even and $0 \le s \le 2m-1$. It is shown that the cross correlation takes at least four values. Furthermore, we confirm the validity of two famous conjectures due to Sarwate et al. and Helleseth in this case.

preprint2012arXiv

Association schemes related to Delsarte-Goethals codes

In this paper, we construct an infinite series of 9-class association schemes from a refinement of the partition of Delsarte-Goethals codes by their Lee weights. The explicit expressions of the dual schemes are determined through direct manipulations of complicated exponential sums. As a byproduct, the other three infinite families of association schemes are also obtained as fusion schemes and quotient schemes.

preprint2012arXiv

Constructions of Strongly Regular Cayley Graphs and Skew Hadamard Difference Sets from Cyclotomic Classes

In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and they generalize the constructions given by Feng and Xiang \cite{FX111,FX113}. Three infinite families of strongly regular graphs with new parameters are obtained. The main tools that we employed are index 2 Gauss sums, instead of cyclotomic numbers.

preprint2012arXiv

The fine triangle intersections for maximum kite packings

In this paper the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let $Fin(v)={(s,t):$ $\exists$ a pair of maximum kite packings of order $v$ intersecting in $s$ blocks and $s+t$ triangles$}$. Let $Adm(v)={(s,t): s+t\leq b_v, s,t$ are non-negative integers$}$, where $b_v=\lfloor v(v-1)/8\rfloor$. It is established that $Fin(v)= Adm(v)\setminus {(b_v-1,0),(b_v-1,1)}$ for any integer $v\equiv 0,1 ({\rm mod} 8)$ and $v\geq 8$; $Fin(v)=Adm(v)$ for any integer $v\equiv 2,3,4,5,6,7 ({\rm mod} 8)$ and $v\geq 4$.

preprint2011arXiv

Exterior algebras and two conjectures on finite abelian groups

Let G be a finite abelian group with |G|>1. Let a_1,...,a_k be k distinct elements of G and let b_1,...,b_k be (not necessarily distinct) elements of G, where k is a positive integer smaller than the least prime divisor of |G|. We show that there is a permutation $π$ on {1,...,k} such that a_1b_{π(1)},...,a_kb_{π(k)} are distinct, provided that any other prime divisor of |G| (if there is any) is greater than k!. This in particular confirms the Dasgupta-Karolyi-Serra-Szegedy conjecture for abelian p-groups. We also pose a new conjecture involving determinants and characters, and show that its validity implies Snevily's conjecture for abelian groups of odd order. Our methods involve exterior algebras and characters.

preprint2011arXiv

Partial difference sets from quadratic forms and $p$-ary weakly regular bent functions

We generalize the construction of affine polar graphs in two different ways to obtain new partial difference sets and amorphic association schemes. The first generalization uses a combination of quadratic forms and uniform cyclotomy. In the second generalization we replace the quadratic form in the affine polar graph construction by higher degree homogeneous functions that are $p$-ary weakly regular bent. The negative Latin square type partial difference sets arising from the first generalization are new.

preprint2010arXiv

Query-Efficient Locally Decodable Codes of Subexponential Length

We develop the algebraic theory behind the constructions of Yekhanin (2008) and Efremenko (2009), in an attempt to understand the ``algebraic niceness'' phenomenon in $\mathbb{Z}_m$. We show that every integer $m = pq = 2^t -1$, where $p$, $q$ and $t$ are prime, possesses the same good algebraic property as $m=511$ that allows savings in query complexity. We identify 50 numbers of this form by computer search, which together with 511, are then applied to gain improvements on query complexity via Itoh and Suzuki's composition method. More precisely, we construct a $3^{\lceil r/2\rceil}$-query LDC for every positive integer $r<104$ and a $\left\lfloor (3/4)^{51}\cdot 2^{r}\right\rfloor$-query LDC for every integer $r\geq 104$, both of length $N_{r}$, improving the $2^r$ queries used by Efremenko (2009) and $3\cdot 2^{r-2}$ queries used by Itoh and Suzuki (2010). We also obtain new efficient private information retrieval (PIR) schemes from the new query-efficient LDCs.