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A predictive model makes outcome predictions based on some given features, i.e., it estimates the conditional probability of the outcome given a feature vector. In general, a predictive model cannot estimate the causal effect of a feature on the outcome, i.e., how the outcome will change if the feature is changed while keeping the values of other features unchanged. This is because causal effect estimation requires interventional probabilities. However, many real world problems such as personalised decision making, recommendation, and fairness computing, need to know the causal effect of any feature on the outcome for a given instance. This is different from the traditional causal effect estimation problem with a fixed treatment variable. This paper first tackles the challenge of estimating the causal effect of any feature (as the treatment) on the outcome w.r.t. a given instance. The theoretical results naturally link a predictive model to causal effect estimations and imply that a predictive model is causally interpretable when the conditions identified in the paper are satisfied. The paper also reveals the robust property of a causally interpretable model. We use experiments to demonstrate that various types of predictive models, when satisfying the conditions identified in this paper, can estimate the causal effects of features as accurately as state-of-the-art causal effect estimation methods. We also show the potential of such causally interpretable predictive models for robust predictions and personalised decision making., Comment: 16

In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded ideal. We also prove that there exist families of cyclic quartic fields which have well-rounded ideals and explicitly construct their minimal bases. In addition, for a given prime number $p$, if a cyclic quartic field has a unique prime ideal above $p$, then we provide the necessary and sufficient conditions for that ideal to be well-rounded. Moreover, in cyclic quartic fields, we provide the prime decomposition of all odd prime numbers and construct an explicit integral basis for every prime ideal., Comment: 42 pages

In this paper, we investigate the size function $h^0$ for number fields. This size function is analogous to the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. Van der Geer and Schoof conjectured that $h^0$ attains its maximum at the trivial class of Arakelov divisors. This conjecture was proved for all number fields with unit group of rank 0 and 1, and also for cyclic cubic fields which have unit group of rank two. We prove the conjecture also holds for totally imaginary cyclic sextic fields, another class of number fields with unit group of rank two., Comment: 22 pages

In this paper, we investigate the properties of well-rounded twists of a given ideal lattice of an imaginary quadratic field $K$. We show that every ideal lattice $I$ of $K$ has at least one well-rounded twist lattice. Moreover, we provide an explicit algorithm to compute all well-rounded twists of $I$., Comment: 24 pages

This paper examines the performance of a 2x2 Line of Sight (LoS) Multiple Input Multiple Output (MIMO) channel at three terahertz frequencies-340 GHz, 410 Ghz, and 460 GHz. While theoretical models predict very high channel capacities, we observe lower capacity which is explained by asymmetric transmit-to-receive signal strengths as well as due to signal attenuation over longer distances. Overall, however, we note that at 460 Ghz, channel capacity of higher than 12 bps/hz is possible even at sub-optimal inter-antenna spacings (for different distances). An important observation is also that we need to maintain appropriate receive signal levels at receive antennas in order to improve capacity.

There is a growing interest in exploiting the terahertz frequency band for future communication systems that demand high data rates. Given the complex propagation behavior of this frequency band, various researchers have developed channel models that can be utilized in the development of communication systems. These models however do not include a crucial aspect of terahertz propagation at short distances: the presence of standing waves. Our measurements show that at specific distances, the effect of standing waves is significant. In this paper, we extend previous terahertz channel models to include the effect of standing waves and show a good fit with our measurements. Our measurements and modeling cover the five most promising terahertz frequency bands: 140, 220, 340, 410, 460 GHz., Comment: IEEE ICC 2021 4th IEEE International Workshop on Terahertz Communications, June 2021

Terahertz frequencies are an untapped resource for providing high-speed short-range communications. As a result, it is of interest to study the propagation characteristics of terahertz waves and to develop channel models. In previous work we used a measurement-based approach to develop an accurate channel model for line of sight (LoS) links. In this paper we extend that work by developing channel models for non-line of sight (NLoS) links where the signal suffers one reflection. We study reflections that occur off a metal plate as well as a piece of wood. Our model for received magnitude includes the effects of standing waves that develop between the transmitter and receiver. Measurements show an excellent agreement between empirical data and the model. In addition, we have analyzed the received phase of the reflected signal at frequencies in the range 320- 480 GHz. We observed a linear error between the predicted and actual phase and developed a model to accommodate that discrepancy. The final model we have developed for predicting received phase is very accurate for the entire range 320 - 480 GHz and for both materials.

This paper studies the problem of estimating the contributions of features to the prediction of a specific instance by a machine learning model and the overall contribution of a feature to the model. The causal effect of a feature (variable) on the predicted outcome reflects the contribution of the feature to a prediction very well. A challenge is that most existing causal effects cannot be estimated from data without a known causal graph. In this paper, we define an explanatory causal effect based on a hypothetical ideal experiment. The definition brings several benefits to model agnostic explanations. First, explanations are transparent and have causal meanings. Second, the explanatory causal effect estimation can be data driven. Third, the causal effects provide both a local explanation for a specific prediction and a global explanation showing the overall importance of a feature in a predictive model. We further propose a method using individual and combined variables based on explanatory causal effects for explanations. We show the definition and the method work with experiments on some real-world data sets., Comment: 17

The paper concerns several theoretical aspects of oriented supersingular $\ell$-isogeny volcanoes and their relationship to closed walks in the supersingular $\ell$-isogeny graph. Our main result is a bijection between the rims of the union of all oriented supersingular $\ell$-isogeny volcanoes over $\overline{\mathbb{F}}_p$ (up to conjugation of the orientations), and isogeny cycles (non-backtracking closed walks which are not powers of smaller walks) of the supersingular $\ell$-isogeny graph over $\overline{\mathbb{F}}_p$. The exact proof and statement of this bijection are made more intricate by special behaviours arising from extra automorphisms and the ramification of $p$ in certain quadratic orders. We use the bijection to count isogeny cycles of given length in the supersingular $\ell$-isogeny graph exactly as a sum of class numbers of these orders, and also give an explicit upper bound by estimating the class numbers., Comment: 41 pages, 7 figures

In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is known that a small endomorphism enables polynomial-time path-finding and endomorphism ring computation (Love-Boneh [36]). An endomorphism gives an explicit orientation of a supersingular elliptic curve. In this paper, we use the volcano structure of the oriented supersingular isogeny graph to take ascending/descending/horizontal steps on the graph and deduce path-finding algorithms to an initial curve. Each altitude of the volcano corresponds to a unique quadratic order, called the primitive order. We introduce a new hard problem of computing the primitive order given an arbitrary endomorphism on the curve, and we also provide a sub-exponential quantum algorithm for solving it. In concurrent work (Wesolowski [54]), it was shown that the endomorphism ring problem in the presence of one endomorphism with known primitive order reduces to a vectorization problem, implying path-finding algorithms. Our path-finding algorithms are more general in the sense that we don't assume the knowledge of the primitive order associated with the endomorphism., Comment: 40 pages, 1 figure; 3rd revision implements small corrections and expositional improvements

We consider the Grothendieck polynomials appearing in the K-theory of Grassmannians, which are analogs of Schur polynomials. This paper aims to establish a version of the Murnaghan-Nakayama rule for Grothendieck polynomials of the Grassmannian type. This rule allows us to express the product of a Grothendieck polynomial with a power sum symmetric polynomial into a linear combination of other Grothendieck polynomials., Comment: 12 pages, 8 figures

Blind signatures play an important role in both electronic cash and electronic voting systems. Blind signatures should be secure against various attacks (such as signature forgeries). The work puts a special attention to secret key exposure attacks, which totally break digital signatures. Signatures that resist secret key exposure attacks are called forward secure in the sense that disclosure of a current secret key does not compromise past secret keys. This means that forward-secure signatures must include a mechanism for secret-key evolution over time periods. This paper gives a construction of the first blind signature that is forward secure. The construction is based on the SIS assumption in the lattice setting. The core techniques applied are the binary tree data structure for the time periods and the trapdoor delegation for the key-evolution mechanism., Comment: ACISP 2020

Federated Learning (FL) has been recently presented as a new technique for training shared machine learning models in a distributed manner while respecting data privacy. However, implementing FL in wireless networks may significantly reduce the lifetime of energy-constrained mobile devices due to their involvement in the construction of the shared learning models. To handle this issue, we propose a novel approach at the physical layer based on the application of lightwave power transfer in the FL-based wireless network and a resource allocation scheme to manage the network's power efficiency. Hence, we formulate the corresponding optimization problem and then propose a method to obtain the optimal solution. Numerical results reveal that, the proposed scheme can provide sufficient energy to a mobile device for performing FL tasks without using any power from its own battery. Hence, the proposed approach can support the FL-based wireless network to overcome the issue of limited energy in mobile devices., Comment: Accepted for publication in IEEE Communications Letters

Breakthroughs in information and power transfer for wireless networks are imperative in order to satisfy the requirement of wireless nodes for energy sustainability. To this end, significant research efforts in academia and industry have been devoted to the design of optimal resource allocation schemes for RF simultaneous wireless information and power transfer (SWIPT) networks. The transmit power constraints imposed by safety regulations introduce significant challenges to the improvement of the power transfer performance. Therefore, solely relying on RF resources to cope with the expectations of next-generation wireless networks, such as longer device lifetimes and higher data rates, may no longer be possible. Thus, the investigation of technologies complementary to conventional RF SWIPT is of critical importance. In this article, we propose a novel collaborative RF and lightwave power transfer technology for future networks, where both the RF and lightwave bands can be entirely exploited. In this context, we introduce the basic transceiver architecture and four corresponding collaborative communication and power transfer protocols. Finally, key potential future research directions are highlighted.