Unrestricted State Complexity of Binary Operations on Regular and Ideal Languages

We study the state complexity of binary operations on regular languages over different alphabets. It is known that if $L'_m$ and $L_n$ are languages of state complexities $m$ and $n$, respectively, and restricted to the same alphabet, the state complexity of any binary boolean operation on $L'_m$ and $L_n$ is $mn$, and that of product (concatenation) is $m 2^n - 2^{n-1}$. In contrast to this, we show that if $L'_m$ and $L_n$ are over different alphabets, the state complexity of union and symmetric difference is $(m+1)(n+1)$, that of difference is $mn+m$, that of intersection is $mn$, and that of product is $m2^n+2^{n-1}$. We also study unrestricted complexity of binary operations in the classes of regular right, left, and two-sided ideals, and derive tight upper bounds. The bounds for product of the unrestricted cases (with the bounds for the restricted cases in parentheses) are as follows: right ideals $m+2^{n-2}+2^{n-1}$ ($m+2^{n-2}$); left ideals $mn+m+n$ ($m+n-1$); two-sided ideals $m+2n$ ($m+n-1$). The state complexities of boolean operations on all three types of ideals are the same as those of arbitrary regular languages, whereas that is not the case if the alphabets of the arguments are the same. Finally, we update the known results about most complex regular, right-ideal, left-ideal, and two-sided-ideal languages to include the unrestricted cases.Comment: 30 pages, 15 figures. This paper is a revised and expanded version of the DCFS 2016 conference paper, also posted previously as arXiv:1602.01387v3. The expanded version has appeared in J. Autom. Lang. Comb. 22 (1-3), 29-59, 2017, the issue of selected papers from DCFS 2016. This version corrects the proof of distinguishability of states in the difference operation on p. 12 in arXiv:1609.04439v

The evolution of gene expression and the transcriptome–phenotype relationship

Changes in gene expression underlie the adaptive evolution in many complex phenotypes, and the recent increase in the availability of multi-species comparative transcriptome data has made it possible to scan whole transcriptomes for loci that have experienced adaptive changes in expression. However, despite the increase in data availability, current models of gene expression evolution often do not account for the complexities and inherent noise associated with transcriptome data. Additionally, in contrast to current models of gene sequence evolution, models of transcriptome evolution often lack the sophistication to effectively determine whether transcriptional differences between species or within a clade are the result of neutral or adaptive processes. In this review, we discuss the tools, methods and models that define our current understanding of the relationship between gene expression and complex phenotype evolution. Our goal is to summarize what we know about the evolution of global gene expression patterns underlying complex traits, as well to identify some of the questions that remain to be answered

Media-Based MIMO: A New Frontier in Wireless Communications

The idea of Media-based Modulation (MBM), is based on embedding information in the variations of the transmission media (channel state). This is in contrast to legacy wireless systems where data is embedded in a Radio Frequency (RF) source prior to the transmit antenna. MBM offers several advantages vs. legacy systems, including "additivity of information over multiple receive antennas", and "inherent diversity over a static fading channel". MBM is particularly suitable for transmitting high data rates using a single transmit and multiple receive antennas (Single Input-Multiple Output Media-Based Modulation, or SIMO-MBM). However, complexity issues limit the amount of data that can be embedded in the channel state using a single transmit unit. To address this shortcoming, the current article introduces the idea of Layered Multiple Input-Multiple Output Media-Based Modulation (LMIMO-MBM). Relying on a layered structure, LMIMO-MBM can significantly reduce both hardware and algorithmic complexities, as well as the training overhead, vs. SIMO-MBM. Simulation results show excellent performance in terms of Symbol Error Rate (SER) vs. Signal-to-Noise Ratio (SNR). For example, a $4\times 16$ LMIMO-MBM is capable of transmitting $32$ bits of information per (complex) channel-use, with SER $\simeq 10^{-5}$ at $E_b/N_0\simeq -3.5$dB (or SER $\simeq 10^{-4}$ at $E_b/N_0=-4.5$dB). This performance is achieved using a single transmission and without adding any redundancy for Forward-Error-Correction (FEC). This means, in addition to its excellent SER vs. energy/rate performance, MBM relaxes the need for complex FEC structures, and thereby minimizes the transmission delay. Overall, LMIMO-MBM provides a promising alternative to MIMO and Massive MIMO for the realization of 5G wireless networks.Comment: 26 pages, 11 figures, additional examples are given to further explain the idea of Media-Based Modulation. Capacity figure adde

Effects of semantic and syntactic complexities and aspectual class on past tense production

This paper reports results from a series of experiments that investigated whether semantic and/or syntactic complexity influences young Dutch children’s production of past tense forms. The constructions used in the three experiments were (i) simple sentences (the Simple Sentence Experiment), (ii) complex sentences with CP complements (the Complement Clause Experiment) and (iii) complex sentences with relative clauses (the Relative Clause Experiment). The stimuli involved both atelic and telic predicates. The goal of this paper is to address the following questions. Q1. Does semantic complexity regarding temporal anchoring influence the types of errors that children make in the experiments? For example, do children make certain types of errors when a past tense has to be anchored to the Utterance Time (UT), as compared to when it has to be anchored to the matrix topic time (TT)? Q2. Do different syntactic positions influence children’s performance on past-tense production? Do children perform better in the Simple Sentence Experiment compared to complex sentences involving two finite clauses (the Complement Clause Experiment and the Relative Clause Experiment)? In complex sentence trials, do children perform differently when the CPs are complements vs. when the CPs are adjunct clauses? (Lebeaux 1990, 2000) Q3. Do Dutch children make more errors with certain types of predicate (such as atelic predicates)? Alternatively, do children produce a certain type of error with a certain type of predicates (such as producing a perfect aspect with punctual predicates)? Bronckart and Sinclair (1973), for example, found that until the age of 6, French children showed a tendency to use passé composé with perfective events and simple present with imperfective events; we will investigate whether or not the equivalent of this is observed in Dutch

Deriving rhetorical complexity data from the RST-DT Corpus

This paper describes a study of the levels at which different rhetorical relations occur in rhetorical structure trees. In a previous empirical study (Williams and Reiter, 2003) of the RST-DT (Rhetorical Structure Theory Discourse Treebank) Corpus (Carlson et al., 2003), we noticed that certain rhetorical relations tended to occur more frequently at higher levels in a rhetorical structure tree, whereas others seemed to occur more often at lower levels. The present study takes a closer look at the data, partly to test this observation, and partly to investigate related issues such as the relative complexity of satellite and nucleus for each type of relation. One practical application of this investigation would be to guide discourse planning in Natural Language Generation (NLG), so that it reflects more accurately the structures found in documents written by human authors. We present our preliminary findings and discuss their relevance for discourse planning

Entanglement, quantum randomness, and complexity beyond scrambling

Scrambling is a process by which the state of a quantum system is effectively randomized due to the global entanglement that "hides" initially localized quantum information. In this work, we lay the mathematical foundations of studying randomness complexities beyond scrambling by entanglement properties. We do so by analyzing the generalized (in particular R\'enyi) entanglement entropies of designs, i.e. ensembles of unitary channels or pure states that mimic the uniformly random distribution (given by the Haar measure) up to certain moments. A main collective conclusion is that the R\'enyi entanglement entropies averaged over designs of the same order are almost maximal. This links the orders of entropy and design, and therefore suggests R\'enyi entanglement entropies as diagnostics of the randomness complexity of corresponding designs. Such complexities form a hierarchy between information scrambling and Haar randomness. As a strong separation result, we prove the existence of (state) 2-designs such that the R\'enyi entanglement entropies of higher orders can be bounded away from the maximum. However, we also show that the min entanglement entropy is maximized by designs of order only logarithmic in the dimension of the system. In other words, logarithmic-designs already achieve the complexity of Haar in terms of entanglement, which we also call max-scrambling. This result leads to a generalization of the fast scrambling conjecture, that max-scrambling can be achieved by physical dynamics in time roughly linear in the number of degrees of freedom.Comment: 72 pages, 4 figures. Rewritten version with new title. v3: published versio

Structure and Function of Iron-Loaded Synthetic Melanin

We describe a synthetic method for increasing and controlling the iron loading of synthetic melanin nanoparticles and use the resulting materials to perform a systematic quantitative investigation on their structure 12property relationship. A comprehensive analysis by magnetometry, electron paramagnetic resonance, and nuclear magnetic relaxation dispersion reveals the complexities of their magnetic behavior and how these intraparticle magnetic interactions manifest in useful material properties such as their performance as MRI contrast agents. This analysis allows predictions of the optimal iron loading through a quantitative modeling of antiferromagnetic coupling that arises from proximal iron ions. This study provides a detailed understanding of this complex class of synthetic biomaterials and gives insight into interactions and structures prevalent in naturally occurring melanins