The Theory Behind TheoryMine

Abstract. We describe the technology behind the TheoryMine novelty gift company, which sells the rights to name novel mathematical theorems. A tower of four computer systems is used to generate recursive theories, then to speculate conjectures in those theories and then to prove these conjectures. All stages of the process are entirely automatic. The process guarantees large numbers of sound, novel theorems of some intrinsic merit.

MATHsAiD: Automated Mathematical Theory Exploration

The aim of the MATHsAiD project is to build a tool for automated theorem-discovery; to design and build a tool to automatically conjecture and prove theorems (lemmas, corollaries, etc.) from a set of user-supplied axioms and definitions. No other input is required. This tool would, for instance, allow a mathematician to try several versions of a particular definition, and in a relatively small amount of time, be able to see some of the consequences, in terms of the resulting theorems, of each version. Moreover, the automatically discovered theorems could perhaps help the users to discover and prove further theorems for themselves. The tool could also easily be used by educators (to generate exercise sets, for instance) and by students as well. In a similar fashion, it might also prove useful in enabling automated theorem provers to dispatch many of the more difficult proof obligations arising in software verification, by automatically generating lemmas which are needed by the prover, in order to finish these proofs

Perception of clear fricatives by normal-hearing and simulated hearing-impaired listeners

This is the publisher's version, also available electronically from http://scitation.aip.org/content/asa/journal/jasa/123/2/10.1121/1.2821966.Speakers may adapt the phonetic details of their productions when they anticipate perceptual difficulty or comprehension failure on the part of a listener. Previous research suggests that a speaking style known as clear speech is more intelligible overall than casual, conversational speech for a variety of listener populations. However, it is unknown whether clear speech improves the intelligibility of fricative consonants specifically, or how its effects on fricative perception might differ depending on listener population. The primary goal of this study was to determine whether clear speech enhances fricative intelligibility for normal-hearing listeners and listeners with simulated impairment. Two experiments measured babble signal-to-noise ratio thresholds for fricative minimal pair distinctions for 14 normal-hearing listeners and 14 listeners with simulated sloping, recruiting impairment. Results indicated that clear speech helped both groups overall. However, for impaired listeners, reliable clear speech intelligibility advantages were not found for non-sibilant pairs. Correlation analyses comparing acoustic and perceptual data indicated that a shift of energy concentration toward higher frequency regions and greater source strength contributed to the clear speecheffect for normal-hearing listeners. Correlations between acoustic and perceptual data were less consistent for listeners with simulated impairment, and suggested that lower-frequency information may play a role

A compact statistical model of the song syntax in Bengalese finch

Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these complex syllable sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. Here we analyze the song syntax in a Bengalese finch. We show that the Markov model fails to capture the statistical properties of the syllable sequences. Instead, a state transition model that accurately describes the statistics of the syllable sequences includes adaptation of the self-transition probabilities when states are repeatedly revisited, and allows associations of more than one state to the same syllable. Such a model does not increase the model complexity significantly. Mathematically, the model is a partially observable Markov model with adaptation (POMMA). The success of the POMMA supports the branching chain network hypothesis of how syntax is controlled within the premotor song nucleus HVC, and suggests that adaptation and many-to-one mapping from neural substrates to syllables are important features of the neural control of complex song syntax

Bilateral Multi-Electrode Neurophysiological Recordings Coupled to Local Pharmacology in Awake Songbirds

Here we describe a protocol for bilateral multielectrode neurophysiological recordings during intracerebral pharmacological manipulations in awake songbirds. This protocol encompasses fitting adult animals with head-posts and recording chambers, and acclimating them to periods of restraint. The adaptation period is followed by bilateral penetrations of multiple electrodes to obtain acute, sensory-driven neurophysiological responses before versus during the application of pharmacological agents of interest. These local manipulations are achieved by simultaneous and restricted drug infusions carried out independently for each hemisphere. We have used this protocol to elucidate how neurotransmitter and neuroendocrine systems shape the auditory and perceptual processing of natural, learned communication signals. However, this protocol can be used to explore the neurochemical basis of sensory processing in other small vertebrates. Representative results and troubleshooting of key steps of this protocol are presented. Following the animal\u27s recovery from head-post and recording chamber implantation surgery, the length of the procedure is 2 d

Cannabinoid exposure during zebra finch sensorimotor vocal learning persistently alters expression of endocannabinoid signaling elements and acute agonist responsiveness

<p>Abstract</p> <p>Background</p> <p>Previously we have found that cannabinoid treatment of zebra finches during sensorimotor stages of vocal development alters song patterns produced in adulthood. Such persistently altered behavior must be attributable to changes in physiological substrates responsible for song. We are currently working to identify the nature of such physiological changes, and to understand how they contribute to altered vocal learning. One possibility is that developmental agonist exposure results in altered expression of elements of endocannabinoid signaling systems. To test this hypothesis we have studied effects of the potent cannabinoid receptor agonist WIN55212-2 (WIN) on endocannabinoid levels and densities of CB₁immunostaining in zebra finch brain.</p> <p>Results</p> <p>We found that late postnatal WIN treatment caused a long-term global disregulation of both levels of the endocannabinoid, 2-arachidonyl glycerol (2-AG) and densities of CB₁immunostaining across brain regions, while repeated cannabinoid treatment in adults produced few long-term changes in the endogenous cannabinoid system.</p> <p>Conclusions</p> <p>Our findings indicate that the zebra finch endocannabinoid system is particularly sensitive to exogenous agonist exposure during the critical period of song learning and provide insight into susceptible brain areas.</p

Characterization of Synaptically Connected Nuclei in a Potential Sensorimotor Feedback Pathway in the Zebra Finch Song System

Birdsong is a learned behavior that is controlled by a group of identified nuclei, known collectively as the song system. The cortical nucleus HVC (used as a proper name) is a focal point of many investigations as it is necessary for song production, song learning, and receives selective auditory information. HVC receives input from several sources including the cortical area MMAN (medial magnocellular nucleus of the nidopallium). The MMAN to HVC connection is particularly interesting as it provides potential sensorimotor feedback to HVC. To begin to understand the role of this connection, we investigated the physiological relation between MMAN and HVC activity with simultaneous multiunit extracellular recordings from these two nuclei in urethane anesthetized zebra finches. As previously reported, we found similar timing in spontaneous bursts of activity in MMAN and HVC. Like HVC, MMAN responds to auditory playback of the bird's own song (BOS), but had little response to reversed BOS or conspecific song. Stimulation of MMAN resulted in evoked activity in HVC, indicating functional excitation from MMAN to HVC. However, inactivation of MMAN resulted in no consistent change in auditory responses in HVC. Taken together, these results indicate that MMAN provides functional excitatory input to HVC but does not provide significant auditory input to HVC in anesthetized animals. We hypothesize that MMAN may play a role in motor reinforcement or coordination, or may provide modulatory input to the song system about the internal state of the animal as it receives input from the hypothalamus

A Potential Neural Substrate for Processing Functional Classes of Complex Acoustic Signals

Categorization is essential to all cognitive processes, but identifying the neural substrates underlying categorization processes is a real challenge. Among animals that have been shown to be able of categorization, songbirds are particularly interesting because they provide researchers with clear examples of categories of acoustic signals allowing different levels of recognition, and they possess a system of specialized brain structures found only in birds that learn to sing: the song system. Moreover, an avian brain nucleus that is analogous to the mammalian secondary auditory cortex (the caudo-medial nidopallium, or NCM) has recently emerged as a plausible site for sensory representation of birdsong, and appears as a well positioned brain region for categorization of songs. Hence, we tested responses in this non-primary, associative area to clear and distinct classes of songs with different functions and social values, and for a possible correspondence between these responses and the functional aspects of songs, in a highly social songbird species: the European starling. Our results clearly show differential neuronal responses to the ethologically defined classes of songs, both in the number of neurons responding, and in the response magnitude of these neurons. Most importantly, these differential responses corresponded to the functional classes of songs, with increasing activation from non-specific to species-specific and from species-specific to individual-specific sounds. These data therefore suggest a potential neural substrate for sorting natural communication signals into categories, and for individual vocal recognition of same-species members. Given the many parallels that exist between birdsong and speech, these results may contribute to a better understanding of the neural bases of speech

A reafferent and feed-forward model of song syntax generation in the Bengalese finch

Adult Bengalese finches generate a variable song that obeys a distinct and individual syntax. The syntax is gradually lost over a period of days after deafening and is recovered when hearing is restored. We present a spiking neuronal network model of the song syntax generation and its loss, based on the assumption that the syntax is stored in reafferent connections from the auditory to the motor control area. Propagating synfire activity in the HVC codes for individual syllables of the song and priming signals from the auditory network reduce the competition between syllables to allow only those transitions that are permitted by the syntax. Both imprinting of song syntax within HVC and the interaction of the reafferent signal with an efference copy of the motor command are sufficient to explain the gradual loss of syntax in the absence of auditory feedback. The model also reproduces for the first time experimental findings on the influence of altered auditory feedback on the song syntax generation, and predicts song- and species-specific low frequency components in the LFP. This study illustrates how sequential compositionality following a defined syntax can be realized in networks of spiking neurons