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Nan Liu

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Published work

26 published item(s)

preprint2026arXiv

Resolving the bias-precision paradox with stochastic causal representation learning for personalized medicine

Estimating individualized treatment effects from longitudinal observational data is central to data-driven medicine, yet existing methods face a fundamental limitation: reducing confounding bias often suppresses clinically informative heterogeneity, degrading patient-specific predictions. Here, we identify this tension as a bias-precision paradox in causal representation learning and introduce sampling-based maximum mean discrepancy (sMMD), a stochastic alignment strategy that replaces global adversarial balancing with subset-level matching. We instantiate this approach in a framework for counterfactual outcome prediction with attribution-grounded interpretability. Across two large-scale ICU cohorts (n = 27,783), our framework improves accuracy under distribution shift, reducing error by up to 11.5% and substantially increasing recall in high-risk tasks. Mechanistic analyses show that sMMD selectively preserves clinically decisive variables. In human-AI evaluation, our method outperforms clinicians-in-training and large language models, and improves clinician accuracy by 14.7% while reducing decision time, enabling interpretable, real-time clinical decision support.

preprint2023arXiv

A Framework for Mutual Information-based MIMO Integrated Sensing and Communication Beamforming Design

Integrated sensing and communication (ISAC) unifies sensing and communication, and improves the efficiency of the spectrum, energy, and hardware. In this work, we investigate the ISAC beamforming design to maximize the mutual information between the target response matrix of a point radar target and the echo signals, while ensuring the data rate requirements of the communication users. In order to study the impact of the echo interference caused by communication users on sensing performance, we study two scenarios: a single communication user and multiple communication users. For the case of a single communication user, we consider three types of echo interference, no interference, a point interference, and an extended interference. For the case of multiple communication users, the interference is also an extended one, and furthermore, each user's communication rate requirement needs to be satisfied. To find the optimal beamforming design in these problems, we provide a closed-form solution with low complexiy, a semidefinite relaxation (SDR) method, a low-complexity algorithm based on the Majorization-Minimization (MM) method and the successive convex approximation (SCA) method, and an algorithm based on MM method and SCA method, respectively. Numerical results demonstrate that, compared to the ISAC beamforming schemes based on the Cramér-Rao bound (CRB) metric and the beampattern metric, the proposed mutual information metric can bring better beampattern and root mean square error (RMSE) of angle estimation. Furthermore, our proposed schemes designed based on the mutual information metric can suppress the echo interference from the communication users effectively.

preprint2023arXiv

Compositional Visual Generation with Composable Diffusion Models

Large text-guided diffusion models, such as DALLE-2, are able to generate stunning photorealistic images given natural language descriptions. While such models are highly flexible, they struggle to understand the composition of certain concepts, such as confusing the attributes of different objects or relations between objects. In this paper, we propose an alternative structured approach for compositional generation using diffusion models. An image is generated by composing a set of diffusion models, with each of them modeling a certain component of the image. To do this, we interpret diffusion models as energy-based models in which the data distributions defined by the energy functions may be explicitly combined. The proposed method can generate scenes at test time that are substantially more complex than those seen in training, composing sentence descriptions, object relations, human facial attributes, and even generalizing to new combinations that are rarely seen in the real world. We further illustrate how our approach may be used to compose pre-trained text-guided diffusion models and generate photorealistic images containing all the details described in the input descriptions, including the binding of certain object attributes that have been shown difficult for DALLE-2. These results point to the effectiveness of the proposed method in promoting structured generalization for visual generation. Project page: https://energy-based-model.github.io/Compositional-Visual-Generation-with-Composable-Diffusion-Models/

preprint2022arXiv

AutoScore-Ordinal: An interpretable machine learning framework for generating scoring models for ordinal outcomes

Background: Risk prediction models are useful tools in clinical decision-making which help with risk stratification and resource allocations and may lead to a better health care for patients. AutoScore is a machine learning-based automatic clinical score generator for binary outcomes. This study aims to expand the AutoScore framework to provide a tool for interpretable risk prediction for ordinal outcomes. Methods: The AutoScore-Ordinal framework is generated using the same 6 modules of the original AutoScore algorithm including variable ranking, variable transformation, score derivation (from proportional odds models), model selection, score fine-tuning, and model evaluation. To illustrate the AutoScore-Ordinal performance, the method was conducted on electronic health records data from the emergency department at Singapore General Hospital over 2008 to 2017. The model was trained on 70% of the data, validated on 10% and tested on the remaining 20%. Results: This study included 445,989 inpatient cases, where the distribution of the ordinal outcome was 80.7% alive without 30-day readmission, 12.5% alive with 30-day readmission, and 6.8% died inpatient or by day 30 post discharge. Two point-based risk prediction models were developed using two sets of 8 predictor variables identified by the flexible variable selection procedure. The two models indicated reasonably good performance measured by mean area under the receiver operating characteristic curve (0.785 and 0.793) and generalized c-index (0.737 and 0.760), which were comparable to alternative models. Conclusion: AutoScore-Ordinal provides an automated and easy-to-use framework for development and validation of risk prediction models for ordinal outcomes, which can systematically identify potential predictors from high-dimensional data.

preprint2022arXiv

Balanced background and explanation data are needed in explaining deep learning models with SHAP: An empirical study on clinical decision making

Objective: Shapley additive explanations (SHAP) is a popular post-hoc technique for explaining black box models. While the impact of data imbalance on predictive models has been extensively studied, it remains largely unknown with respect to SHAP-based model explanations. This study sought to investigate the effects of data imbalance on SHAP explanations for deep learning models, and to propose a strategy to mitigate these effects. Materials and Methods: We propose to adjust class distributions in the background and explanation data in SHAP when explaining black box models. Our data balancing strategy is to compose background data and explanation data with an equal distribution of classes. To evaluate the effects of data adjustment on model explanation, we propose to use the beeswarm plot as a qualitative tool to identify "abnormal" explanation artifacts, and quantitatively test the consistency between variable importance and prediction power. We demonstrated our proposed approach in an empirical study that predicted inpatient mortality using the Medical Information Mart for Intensive Care (MIMIC-III) data and a multilayer perceptron. Results: Using the data balancing strategy would allow us to reduce the number of the artifacts in the beeswarm plot, thus mitigating the negative effects of data imbalance. Additionally, with the balancing strategy, the top-ranked variables from the corresponding importance ranking demonstrated improved discrimination power. Discussion and Conclusion: Our findings suggest that balanced background and explanation data could help reduce the noise in explanation results induced by skewed data distribution and improve the reliability of variable importance ranking. Furthermore, these balancing procedures improve the potential of SHAP in identifying patients with abnormal characteristics in clinical applications.

preprint2022arXiv

Slow Neutron-Capture Process: Low-mass AGB stars and presolar silicon carbide grains

Presolar grains are microscopic dust grains that formed in the stellar winds or explosions of ancient stars that died before the formation of the solar system. The majority (~90% in number) of presolar silicon carbide (SiC) grains, including types mainstream (MS), Y, and Z, came from low-mass C-rich asymptotic giant branch (AGB) stars, which is supported by the ubiquitous presence of SiC dust observed in the circumstellar envelope of AGB stars and the signatures of slow neutron-capture process preserved in these grains. Here, we review the status of isotope studies of presolar AGB SiC grains with an emphasis on heavy-element isotopes and highlight the importance of presolar grain studies for nuclear astrophysics. We discuss the sensitives of different types of nuclei to varying AGB stellar parameters and how their abundances in presolar AGB SiC grains can be used to provide independent, detailed constraints on stellar parameters, including 13C formation, stellar temperature, and nuclear reaction rates.

preprint2022arXiv

Towards Practical Differential Privacy in Data Analysis: Understanding the Effect of Epsilon on Utility in Private ERM

In this paper, we focus our attention on private Empirical Risk Minimization (ERM), which is one of the most commonly used data analysis method. We take the first step towards solving the above problem by theoretically exploring the effect of epsilon (the parameter of differential privacy that determines the strength of privacy guarantee) on utility of the learning model. We trace the change of utility with modification of epsilon and reveal an established relationship between epsilon and utility. We then formalize this relationship and propose a practical approach for estimating the utility under an arbitrary value of epsilon. Both theoretical analysis and experimental results demonstrate high estimation accuracy and broad applicability of our approach in practical applications. As providing algorithms with strong utility guarantees that also give privacy when possible becomes more and more accepted, our approach would have high practical value and may be likely to be adopted by companies and organizations that would like to preserve privacy but are unwilling to compromise on utility.

preprint2021arXiv

Oxygen and Aluminum-Magnesium Isotopic Systematics of Presolar Nanospinel Grains from CI Chondrite Orgueil

Presolar oxide grains have been previously divided into several groups (Group 1 to 4) based on their isotopic compositions, which can be tied to several stellar sources. Much of available data was acquired on large grains, which may not be fully representative of the presolar grain population present in meteorites. We present here new O isotopic data for 74 small presolar oxide grains (~200 nm in diameter on average) from Orgueil and Al-Mg isotopic systematics for 25 of the grains. Based on data-model comparisons, we show that (i) Group 1 and Group 2 grains more likely originated in low-mass first-ascent (red giant branch; RGB) and/or second-ascent (asymptotic giant branch; AGB) red giant stars and (ii) Group 1 grains with (26Al/27Al)0 >= 5x10^-3 and Group 2 grains with (26Al/27Al)0 <= 1x10^-2 all likely experienced extra circulation processes in their parent low-mass stars but under different conditions, resulting in proton-capture reactions occurring at enhanced temperatures. We do not find any large 25Mg excess in Group 1 oxide grains with large 17O enrichments, which provides evidence that 25Mg is not abundantly produced in low-mass stars. We also find that our samples contain a larger proportion of Group 4 grains than so far suggested in the literature for larger presolar oxide grains (~400 nm). We also discuss our observations in the light of stellar dust production mechanisms.

preprint2020arXiv

Cluster analysis of presolar silicon carbide grains: evaluation of their classification and astrophysical implications

Cluster analysis of presolar silicon carbide grains based on literature data for 12C/13C, 14N/15N, δ30Si/28Si, and δ29Si/28Si including or not inferred initial 26Al/27Al data, reveals nine clusters agreeing with previously defined grain types but also highlighting new divisions. Mainstream grains reside in three clusters probably representing different parent star metallicities. One of these clusters has a compact core, with a narrow range of composition, pointing to an enhanced production of SiC grains in asymptotic giant branch (AGB) stars with a narrow range of masses and metallicities. The addition of 26Al/27Al data highlights a cluster of mainstream grains, enriched in 15N and 26Al, which cannot be explained by current AGB models. We defined two AB grain clusters, one with 15N and 26Al excesses, and the other with 14N and smaller 26Al excesses, in agreement with recent studies. Their definition does not use the solar N isotopic ratio as a divider, and the contour of the 26Al-rich AB cluster identified in this study is in better agreement with core-collapse supernova models. We also found a cluster with a mixture of putative nova and AB grains, which may have formed in supernova or nova environments. X grains make up two clusters, having either strongly correlated Si isotopic ratios or deviating from the 2/3 slope line in the Si 3-isotope plot. Finally, most Y and Z grains are jointly clustered, suggesting that the previous use of 12C/13C= 100 as a divider for Y grains was arbitrary. Our results show that cluster analysis is a powerful tool to interpret the data in light of stellar evolution and nucleosynthesis modelling and highlight the need of more multi-element isotopic data for better classification.

preprint2020arXiv

Magnetic-buoyancy Induced Mixing in AGB Stars: Presolar SiC Grains

Isotope ratios can be measured in presolar SiC grains from ancient Asymptotic Giant Branch (AGB) stars at permil-level (0.1\%) precision. Such precise grain data permit derivation of more stringent constraints and calibrations on mixing efficiency in AGB models than traditional spectroscopic observations. In this paper we compare SiC heavy-element isotope ratios to a new series of FRUITY models that include the effects of mixing triggered by magnetic fields. Based on 2D and 3D simulations available in the literature, we propose a new formulation, upon which the general features of mixing induced by magnetic fields can be derived. The efficiency of such a mixing, on the other hand, relies on physical quantities whose values are poorly constrained. We present here our calibration by comparing our model results with the heavy-element isotope data of presolar SiC grains from AGB stars. We demonstrate that the isotopic compositions of all measured elements (Ni, Sr, Zr, Mo, Ba) can be simultaneously fitted by adopting a single magnetic field configuration in our new FRUITY models.

preprint2020arXiv

The Capacity of Private Information Retrieval Under Arbitrary Collusion Patterns

We study the private information retrieval (PIR) problem under arbitrary collusion pattern for replicated databases. We find its capacity, which is the same as the capacity of the original PIR problem with the number of databases $N$ replaced by a number $S^*$. The number $S^*$ is the optimal solution to a linear programming problem that is a function of the collusion pattern. Hence, the collusion pattern affects the capacity of the PIR problem only through the number $S^*$.

preprint2016arXiv

An Upper Bound on the Sum Capacity of the Downlink Multicell Processing with Finite Backhaul Capacity

In this paper, we study upper bounds on the sum capacity of the downlink multicell processing model with finite backhaul capacity for the simple case of 2 base stations and 2 mobile users. It is modelled as a two-user multiple access diamond channel. It consists of a first hop from the central processor to the base stations via orthogonal links of finite capacity, and the second hop from the base stations to the mobile users via a Gaussian interference channel. The converse is derived using the converse tools of the multiple access diamond channel and that of the Gaussian MIMO broadcast channel. Through numerical results, it is shown that our upper bound improves upon the existing upper bound greatly in the medium backhaul capacity range, and as a result, the gap between the upper bounds and the sum rate of the time-sharing of the known achievable schemes is significantly reduced.

preprint2016arXiv

Energy Efficient Transmission for Multicast Services in MISO Distributed Antenna Systems

This paper aims to solve the energy efficiency (EE) maximization problem for multicast services in a multiple-input single-output (MISO) distributed antenna system (DAS). A novel iterative algorithm is proposed, which consists of solving two subproblems iteratively: the power allocation problem and the beam direction updating problem. The former subproblem can be equivalently transformed into a one-dimension quasi-concave problem that is solved by the golden search method. The latter problem can be efficiently solved by the existing method. Simulation results show that the proposed algorithm achieves significant EE performance gains over the existing rate maximization method. In addition, when the backhaul power consumption is low, the EE performance of the DAS is better than that of the centralized antenna system (CAS).

preprint2016arXiv

Stellar Origins of Extremely $^{\text{13}}C$- and $^{15}N$-enriched Presolar SiC Grains: Novae or Supernovae?

Extreme excesses of $^{13}C$ ($^{12}C$/$^{13}C$<10) and $^{15}N$ ($^{14}N$/$^{15}N$<20) in rare presolar SiC grains have been considered diagnostic of an origin in classical novae, though an origin in core collapse supernovae (CCSNe) has also been proposed. We report C, N, and Si isotope data for 14 submicron- to micron-sized $^{13}C$- and $^{15}N$-enriched presolar SiC grains ($^{12}C$/$^{13}C$<16 and $^{14}N$/$^{15}N$<~100) from Murchison, and their correlated Mg-Al, S, and Ca-Ti isotope data when available. These grains are enriched in $^{13}C$ and $^{15}N$, but with quite diverse Si isotopic signatures. Four grains with $^{29,30}Si$ excesses similar to those of type C SiC grains likely came from CCSNe, which experienced explosive H burning occurred during explosions. The independent coexistence of proton- and neutron-capture isotopic signatures in these grains strongly supports heterogeneous H ingestion into the He shell in pre-supernovae. Two of the seven putative nova grains with $^{30}Si$ excesses and $^{29}Si$ depletions show lower-than-solar $^{34}S$/$^{32}S$ ratios that cannot be explained by classical nova nucleosynthetic models. We discuss these signatures within the CCSN scenario. For the remaining five putative nova grains, both nova and supernova origins are viable because explosive H burning in the two stellar sites could result in quite similar proton-capture isotopic signatures. Three of the grains are sub-type AB grains that are also $^{13}C$ enriched, but have a range of higher $^{14}N$/$^{15}N$. We found that $^{15}N$-enriched AB grains (~50<$^{14}N$/$^{15}N$<~100) have distinctive isotopic signatures compared to putative nova grains, such as higher $^{14}N$/$^{15}N$, lower $^{26}Al$/$^{27}Al$, and lack of $^{30}Si$ excess, indicating weaker proton-capture nucleosynthetic environments.

preprint2015arXiv

Correlated Strontium and Barium Isotopic Compositions of Acid-Cleaned Single Silicon Carbides from Murchison

We present strontium, barium, carbon, and silicon isotopic compositions of 61 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing both strontium and barium contamination. For the first time, by using correlated $^{88}Sr$/$^{86}Sr$ and $^{138}Ba$/$^{136}Ba$ ratios in mainstream SiC grains, we are able to resolve the effect of $^{13}C$ concentration from that of $^{13}C$-pocket mass on s-process nucleosynthesis, which points towards the existence of large $^{13}C$-pockets with low $^{13}C$ concentration in AGB stars. The presence of such large $^{13}$R-pockets with a variety of relatively low $^{13}C$ concentrations seems to require multiple mixing processes in parent AGB stars of mainstream SiC grains.

preprint2015arXiv

Energy Efficiency Optimization for MIMO Distributed Antenna Systems

In this paper, we propose a transmit covariance optimization method to maximize the energy efficiency (EE) for a single-user distributed antenna system, where both the remote access units (RAUs) and the user are equipped with multiple antennas. Unlike previous related works, both the rate requirement and RAU selection are taken into consideration. Here, the total circuit power consumption is related to the number of active RAUs. Given this setup, we first propose an optimal transmit covariance optimization method to solve the EE optimization problem under a fixed set of active RAUs. More specifically, we split this problem into three subproblems, i.e., the rate maximization problem, the EE maximization problem without rate constraint, and the power minimization problem, and each subproblem can be efficiently solved. Then, a novel distance-based RAU selection method is proposed to determine the optimal set of active RAUs. Simulation results show that the performance of the proposed RAU selection is almost identical to the optimal exhaustive search method with significantly reduced computational complexity, and the performance of the proposed algorithm significantly outperforms the existing EE optimization methods.

preprint2015arXiv

Energy-Efficient Data Transmission with A Non-FIFO Packet

This paper investigates the problem of energy-efficient packet transmission with a non-FIFO Packet over a point-to-point additive white Gaussian noise (AWGN) time-invariant channel under the feasibility constraints. More specifically, we consider the scenario where there is a packet that has a deadline that is earlier than that of the previously arrived packet. For this problem, the First-In-First-Out (FIFO) transmission mode adopted in the existing literatures is no longer optimal. We first propose a novel packet split and reorder process which convert the inconsistency in the order of deadlines and arrival instants of the packet sequence into a consistent one. After the split and reorder process, the original problem considered in this paper is transformed into the problem of finding the optimal split factor. We propose an algorithm that finds the split factor which consists of checking four possibilities by applying the existing optimal transmission strategy \emph{"String Tautening"} for FIFO packets. In addition, we prove the optimality of the proposed algorithm in the presence of a non-FIFO packet by exploiting the optimality properties of the most energy efficient transmission strategy. Based on the proposed optimal offline scheme, an efficient online policy which assumes causal arrival information is also studied and shown to achieve a comparable performance to the proposed optimal offline scheme.

preprint2015arXiv

Energy-Efficient Data Transmission with Non-FIFO Packets

This paper investigates the problem of energy-efficient packet transmission with arbitrary arrival instants and deadline constraints over a point-to-point Additive White Gaussian Noise (AWGN) channel. This is different from previous work where it is assumed that the packets follow a First-In-First-Out (FIFO) order in that the packets that arrive earlier will have a deadline that is also earlier. We first investigate the necessary and sufficient conditions of the optimal transmission scheduler. We then propose an algorithm which finds the transmission schedule of each packet in the order of the packets with the largest transmission rate to the packets with the smallest transmission rate. Finally, we show that our algorithm satisfies the sufficient conditions of the optimal transmission scheduler and thus, is optimal.

preprint2015arXiv

The $^{13}C$-pockets in AGB Stars and Their Fingerprints in Mainstream SiC Grains

We identify three isotopic tracers that can be used to constrain the $^{13}C$-pocket and show the correlated isotopic ratios of Sr and Ba in single mainstream presolar SiC grains. These newly measured data can be explained by postprocess AGB model calculations with large $^{13}C$-pockets with a range of relatively low $^{13}C$ concentrations, which may suggest that multiple mixing processes contributed to the $^{13}C$-pocket formation in parent AGB stars.

preprint2015arXiv

The Gaussian Multiple Access Diamond Channel

In this paper, we study the capacity of the diamond channel. We focus on the special case where the channel between the source node and the two relay nodes are two separate links with finite capacities and the link from the two relay nodes to the destination node is a Gaussian multiple access channel. We call this model the Gaussian multiple access diamond channel. We first propose an upper bound on the capacity. This upper bound is a single-letterization of an $n$-letter upper bound proposed by Traskov and Kramer, and is tighter than the cut-set bound. As for the lower bound, we propose an achievability scheme based on sending correlated codes through the multiple access channel with superposition structure. We then specialize this achievable rate to the Gaussian multiple access diamond channel. Noting the similarity between the upper and lower bounds, we provide sufficient and necessary conditions that a Gaussian multiple access diamond channel has to satisfy such that the proposed upper and lower bounds meet. Thus, for a Gaussian multiple access diamond channel that satisfies these conditions, we have found its capacity.

preprint2014arXiv

Barium Isotopic Composition of Mainstream Silicon Carbides from Murchison: Constraints for s-Process Nucleosynthesis in AGB Stars

We present barium, carbon, and silicon isotopic compositions of 38 acid-cleaned presolar SiC grains from Murchison. Comparison with previous data shows that acid washing is highly effective in removing barium contamination. Strong depletions in $δ$($^{138}$Ba/$^{136}$Ba) values are found, down to $-$400 permil, which can only be modeled with a flatter $^{13}$C profile within the $^{13}$C pocket than is normally used. The dependence of $δ$($^{138}$Ba/$^{136}$Ba) predictions on the distribution of $^{13}$C within the pocket in AGB models allows us to probe the $^{13}$C profile within the $^{13}$C pocket and the pocket mass in asymptotic giant branch (AGB) stars. In addition, we provide constraints on the $^{22}$Ne$(α,n)^{25}$Mg rate in the stellar temperature regime relevant to AGB stars, based on $δ$($^{134}$Ba/$^{136}$Ba) values of mainstream grains. We found two nominally mainstream grains with strongly negative $δ$($^{134}$Ba/$^{136}$Ba) values that cannot be explained by any of the current AGB model calculations. Instead, such negative values are consistent with the intermediate neutron capture process ($i$-process), which is activated by the Very Late Thermal Pulse (VLTP) during the post-AGB phase and characterized by a neutron density much higher than the $s$-process. These two grains may have condensed around post-AGB stars. Finally, we report abundances of two $p$-process isotopes, $^{130}$Ba and $^{132}$Ba, in single SiC grains. These isotopes are destroyed in the $s$-process in AGB stars. By comparing their abundances with respect to that of $^{135}$Ba, we conclude that there is no measurable decay of $^{135}$Cs ($t_{1/2}$= 2.3 Ma) to $^{135}$Ba in individual SiC grains, indicating condensation of barium, but not cesium into SiC grains before $^{135}$Cs decayed.

preprint2014arXiv

Deception with Side Information in Biometric Authentication Systems

In this paper, we study the probability of successful deception of an uncompressed biometric authentication system with side information at the adversary. It represents the scenario where the adversary may have correlated side information, e.g.,~a partial finger print or a DNA sequence of a relative of the legitimate user. We find the optimal exponent of the deception probability by proving both the achievability and the converse. Our proofs are based on the connection between the problem of deception with side information and the rate distortion problem with side information at both the encoder and decoder.

preprint2014arXiv

Selective metal deposition at graphene line defects by atomic layer deposition

One-dimensional defects in graphene have strong influence on its physical properties, such as electrical charge transport and mechanical strength. With enhanced chemical reactivity, such defects may also allow us to selectively functionalize the material and systematically tune the properties of graphene. Here we demonstrate the selective deposition of metal at chemical vapour deposited graphene's line defects, notably grain boundaries, by atomic layer deposition. Atomic layer deposition allows us to deposit Pt predominantly on graphene's grain boundaries, folds, and cracks due to the enhanced chemical reactivity of these line defects, which is directly confirmed by transmission electron microscopy imaging. The selective functionalization of graphene defect sites, together with the nanowire morphology of deposited Pt, yields a superior platform for sensing applications. Using Pt-graphene hybrid structures, we demonstrate high-performance hydrogen gas sensors at room temperatures and show its advantages over other evaporative Pt deposition methods, in which Pt decorates graphene surface non-selectively.

preprint2014arXiv

The 13C-Pocket Structure in AGB Models: Constraints from Zirconium Isotope Abundances in Single Mainstream SiC Grains

We present postprocess AGB nucleosynthesis models with different $^{13}$C-pocket internal structures to better explain zirconium isotope measurements in mainstream presolar SiC grains by Nicolussi et al. (1997) and Barzyk et al. (2007). We show that higher-than-solar $^{92}$Zr/$^{94}$Zr ratios can be predicted by adopting a $^{13}$C-pocket with a flat $^{13}$C profile, instead of the previous decreasing-with-depth $^{13}$C profile. The improved agreement between grain data for zirconium isotopes and AGB models provides additional support for a recent proposal of a flat $^{13}$C profile based on barium isotopes in mainstream SiC grains by Liu et al. (2014).

preprint2012arXiv

Capacity Bounds and Exact Results for the Cognitive Z-interference Channel

We study the discrete memoryless Z-interference channel (ZIC) where the transmitter of the pair that suffers from interference is cognitive. We first provide an upper bound on the capacity of this channel. We then show that, when the channel of the transmitter-receiver pair that does not experience interference is deterministic, our proposed upper bound matches the known lower bound provided by Cao and Chen in 2008. The obtained results imply that, unlike in the Gaussian cognitive ZIC, in the considered channel superposition encoding at the non-cognitive transmitter as well as Gel'fand-Pinsker encoding at the cognitive transmitter are needed in order to minimize the impact of interference. As a byproduct of the obtained capacity region, we obtain the capacity under the generalized Gel'fand-Pinsker conditions where a transmitter-receiver pair communicates in the presence of interference noncausally known at the encoder.

preprint2007arXiv

Towards the Secrecy Capacity of the Gaussian MIMO Wire-tap Channel: The 2-2-1 Channel

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wire-tap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.