Orthologic with Axioms

We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras while having polynomial-time equivalence checking that is sound with respect to Boolean algebra semantics. We generalize ortholattice reasoning and obtain an algorithm for proving a larger class of classically valid formulas. As the key result, we analyze a proof system for orthologic augmented with axioms. An important feature of the system is that it limits the number of formulas in a sequent to at most two, which makes the extension with axioms non-trivial. We show a generalized form of cut elimination for this system, which implies a sub-formula property. From there we derive a cubic-time algorithm for provability from axioms, or equivalently, for validity in finitely presented ortholattices. We further show that propositional resolution of width 5 proves all formulas provable in orthologic with axioms. We show that orthologic system subsumes resolution of width 2 and arbitrarily wide unit resolution and is complete for reasoning about generalizations of propositional Horn clauses. Moving beyond ground axioms, we introduce effectively propositional orthologic, presenting its semantics as well as a sound and complete proof system. Our proof system implies the decidability of effectively propositional orthologic, as well as its fixed-parameter tractability for a bounded maximal number of variables in each axiom. As a special case, we obtain a generalization of Datalog with negation and disjunction

Low complexity partial selected mapping for PAPR reduction of OFDM system

International audienceWe present partial blind selected mapping method (P-BSLM) as a probabilistic OFDM-PAPR reduction method. The P-BSLM method generates more candidates than the classical SLM (C-SLM) method while using the same number of IFFT computations. Moreover, common stage computation in an IFFT process can reduce the computational complexity. More candidates increase the PAPR reduction capability, and give a better error performance in the presence of non-linear amplifier. This method has the maximum spectral efficiency without side information, and the phase sequence can be correctly detected using partial blind phase sequence detection

Bit Error Rate Calculation for a Multiband Non Coherent On-Off Keying Demodulation

International audienceThe purpose of this paper is to calculate the bit error rate (BER) of a multiband non coherent on-off keying (OOK) demodulation. The results fit perfectly the simulations of the system. It allows us to study the influence of the filter and the decimation factor on the modulation performance. It is also possible to optimize the system, by means of other criteria (e.g. system complexity, jammer sensitivity) thus avoiding time consuming simulations

Robust Detection of Binary CPMs With Unknown Modulation Index

International audienceWe consider soft-output detection of a binary continuous phase modulation (CPM) generated through a low-cost transmitter, thus characterized by a significant modulation index uncertainty, and sent over a channel affected by phase noise. The proposed detector is designed by adopting a simplified representation of a binary CPM signal with the principal component of its Laurent decomposition and is obtained by using the framework based on factor graphs and the sum-product algorithm. It does not require an explicit estimation of the modulation index nor of the channel phase and is very robust to large uncertainties of the nominal value of the modulation index. Being soft-output in nature, this detector can be employed for iterative detection/decoding of practical coded schemes based on a serial concatenation, possibly through a pseudo-random interleaver, of an outer encoder and a CPM modulation forma

Binary Continuous Phase Modulations Robust to a Modulation Index Mismatch

International audienceWe consider binary continuous phase modulation (CPM) signals used in some recent low-cost and low-power consumption telecommunications standard. When these signals are generated through a low-cost transmitter, the real modulation index can end up being quite different from the nominal value employed at the receiver and a significant performance degradation is observed, unless proper techniques for the estimation and compensation are employed. For this reason, we design new binary schemes with a much higher robustness. They are based on the concatenation of a suitable precoder with binary input and a ternary CPM format. The result is a family of CPM formats whose phase state is constrained to follow a specific evolution. Two of these precoders are considered. We will discuss many aspects related to these schemes, such as the power spectral density, the spectral efficiency, simplified detection, the minimum distance, and the uncoded performance. The adopted precoders do not change the recursive nature of CPM schemes. So these schemes are still suited for serial concatenation, through a pseudo-random interleaver, with an outer channel encoder

Confidence Level for Finite Blocklength Ultra Reliable Communication over Fading Channels

International audienc

Power comparison of different methods to detect genetic effects and gene-environment interactions

Identifying gene-environment (G × E) interactions has become a crucial issue in the past decades. Different methods have been proposed to test for G × E interactions in the framework of linkage or association testing. However, their respective performances have rarely been compared. Using Genetic Analysis Workshop 15 simulated data, we compared the power of four methods: one based on affected sib pairs that tests for linkage and interaction (the mean interaction test) and three methods that test for association and/or interaction: a case-control test, a case-only test, and a log-linear approach based on case-parent trios. Results show that for the particular model of interaction between tobacco use and Locus B simulated here, the mean interaction test has poor power to detect either the genetic effect or the interaction. The association studies, i.e., the log-linear-modeling approach and the case-control method, are more powerful to detect the genetic effect (power of 78% and 95%, respectively) and taking into account interaction moderately increases the power (increase of 9% and 3%, respectively). The case-only design exhibits a 95% power to detect G × E interaction but the type I error rate is increased

AFRP20: New P-Wavespeed Model for the African Mantle Reveals Two Whole-Mantle Plumes Below East Africa and Neoproterozoic Modification of the Tanzania Craton

Africa’s Cenozoic tectonism is often attributed to mantle plumes, particularly below East Africa, but their morphology, number, location, and impact on the African lithosphere are debated. The broad slow wavespeed African Superplume, ubiquitous in large-scale tomographic models, originates below South Africa, reaching the surface somewhere below East Africa. However, whether the diverse East African mantle geochemistry is best reconciled with one heterogeneous upwelling, or current tomographic models lack the resolution to image multiple distinct plumes, remains enigmatic. S-wavespeed tomographic images of Africa are legion, but higher-frequency P-wavespeed whole-mantle models possessing complementary diagnostic capabilities are comparatively lacking. This hinders attempts to disentangle the effects of Cenozoic hotspot tectonism and Pan African (and older) tectonic events on the East African lithosphere. Here we develop a continental-scale P-wave tomographic model capable of resolving structure from upper-to-lower mantle depths using a recently-developed technique to extract absolute arrival-times from noisy, temporary African seismograph deployments. Shallow-mantle wavespeeds are δVP ≈–4% below Ethiopia, but less anomalous (δVP ≥–2%) below other volcanic provinces. The heterogeneous African Superplume reaches the upper mantle below the Kenyan plateau. Below Ethiopia/Afar we image a second sub-vertical slow wavespeed anomaly rooted near the core-mantle boundary outside the African LLVP, meaning multiple disparately sourced whole-mantle plumes may influence East African magmatism. In contrast to other African cratons, wavespeeds below Tanzania are only fast to 90–135km depth. When interpreted alongside Lower Eocene on-craton kimberlites, our results support pervasive metasomatic lithospheric modification caused by subduction during the Neoproterozoic Pan-African orogeny.A. B. and S. C. are funded by the Natural Environment Research Council (NERC) Grant number NE/R010862/1 from PI Cottaar in Cambridge. A. B. was previously funded by the NERC Doctoral Training Partnership: Science and Solutions for a Changing Planet - Grant number NE/L002515/1 at Imperial College. I. B is funded by Natural Environment Research Council Grant number NE/S014136/1