kolmogorov complexity and the recursion theorem several classes of diagonally nonrecursive dnr functions are characterized in terms of kolmogorov complexity in particular a set of natural numbers a can wtt compute a dnr function iff there is a nontrivial recursive lower bound on the kolmogorov complexity of the initial segments of a furthermore a can turing compute a dnr function iff there is a nontrivial a recursive lower bound on the kolmogorov complexity of the initial segments of a a is pa complete that is a can compute a 0 1 valued dnr function iff a can compute a function f such that f n is a string of length n and maximal c complexity among the strings of length n a t k iff a can compute a function f such that f n is a string of length n and maximal h complexity among the strings of length n further characterizations for these classes are given the existence of a dnr function in a turing degree is equivalent to the failure of the recursion theorem for this degree thus the provided results characterize those turing degrees in terms of kolmogorov complexity which no longer permit the usage of the recursion theorem

computing the visual hull of solids of revolution abstract the visual hull vh s v of an object s relative to a viewing region v is a geometric entity useful for silhouette based image understanding for instance two objects can be distinguished from their silhouettes only if their visual hulls are different an object can be exactly reconstructed from its silhouettes only if equal to its visual hull the visual hull idea also allows to define a measure of the reconstruction accuracy of an object from its silhouettes there are two main cases of visual hull the internal visual hull if v is only bounded by s and the external visual hull if v is bounded by the convex hull of s this paper addresses the problem of computing both visual hulls of solids of revolution two cases are considered smooth polynomial and piecewise linear generators the algorithm has been implemented for the latter case the surface of the visual hulls when it is not coincident with the surface of s turns out to consist of segments of cones annular rings and hyperboloids of one sheet

fine structure of the 2f1 f2 acoustic distortion product changes with primary level the fine frequency structure of the 2f1 f2 acoustic distortion product adp fine structure was examined in ten human subjects with normal hearing primary frequencies f1 and f2 were incremented in steps of 1 32 octave with an f2 f1 ratio of 1 2 the primary levels were kept equal to each other and varied from 45 to 65 db spl in 2 5 db steps the results show that the adp fine structure is characterized by a series of peaks and valleys across frequency with a peak to peak frequency spacing of about 3 32 octave and a peak to valley amplitude ratio of up to 20 db at frequencies below 4000 hz as primary level increases the sharpness of the adp fine structure is not significantly reduced and the pattern gradually shifts to lower frequencies at frequencies above 4000 hz a flattening of the pattern is sometimes observed at high levels a consequence of the underlying process responsible for the fine structure is that adp input output i o functions can be highly variable in shape dramatic shape change

universal computably enumerable sets and initial segment prefix free complexity we show that there are turing complete computably enumerable sets of arbitrarily low nontrivial initial segment prefix free complexity in particular given any computably enumerable set a with nontrivial prefix free initial segment complexity there exists a turing complete computably enumerable set b with complexity strictly less than the complexity of a on the other hand it is known that sets with trivial initial segment prefix free complexity are not turing complete moreover we give a generalization of this result for any finite collection of computably enumerable sets a i i

reducing reflected contributions to ear canal distortion product otoacoustic emissions in humans distortion product otoacoustic emission dpoae fine structure has been attributed to the interaction of two cochlear source mechanisms distortion and reflection sources a suppressor presented near the 2f1 f2 frequency reduces the reflection source contribution and therefore dpoae fine structure optimal relationships between stimulus and suppressor conditions however have not been described in this study the relationship between suppressor level l3 and stimulus level l2 was evaluated to determine the l3 that was most effective at reducing fine structure subjects were initially screened to find individuals who produced dpoae fine structure a difference in the prevalence of fine structure in two frequency intervals was observed at 2 khz 11 of 12 subjects exhibited fine structure as compared to 5 of 22 subjects at 4 khz only subjects demonstrating fine structure participated in subsequent measurements dpoae responses were evaluated in 1 3 octave intervals centered at 2 or 4 khz with 4 subjects contributing data at each interval multiple l3 s were evaluated for each l2 which ranged from 20 to 80 db spl the results indicated that one or more l3 s at each l2 were roughly equally effective at reducing dpoae fine structure however no single l3 was effective at all l2 s in every subject

measuring distortion product otoacoustic emissions using continuously sweeping primaries distortion product otoacoustic emission dpoae level from normal hearing individuals can vary by as much as 30db with small frequency changes a phenomenon known as dpoae fine structure this fine structure is hypothesized to stem from the interaction of components from two different regions of the cochlea the nonlinear generator region and the reflection component from the dp region an efficient procedure to separate these two components would improve the clinical and research utility of dpoae by permitting separate evaluation of different cochlea regions in this paper two procedures for evaluating dpoae fine structure are compared dpoae generated by fixed frequency primaries versus continuously sweeping primaries the sweep dpoae data are analyzed with a least squares fit filter sweep rates of greater than 8s per octave permit rapid evaluation of the cochlear fine structure a higher sweep rate of 2s per octave provided dpoae without fine structure under these conditions the longer latency reflection component falls outside the range of the filter consequently dpoae obtained with sweeping tones can be used either to get more rapid estimates of dpoae fine structure or to obtain estimates of dpoae from the generator region uncontaminated by energy from the reflection region

on initial segment complexity and degrees of randomness one approach to understanding the fine structure of initial segment complexity was introduced by downey hirschfeldt and laforte they define x k y to mean that vn k x n k y n 0 1 the equivalence classes under this relation are the k degrees we prove that if x y is 1 random then x and y have no upper bound in the k degrees hence no join we also prove that n randomness is closed upward in the k degrees our main tool is another structure intended to measure the degree of randomness of real numbers the vl degrees unlike the k degrees many basic properties of the vl degrees are easy to prove we show that x k y implies x vl y so some results can be transferred the reverse implication is proved to fail the same analysis is also done for c the analogue of k for plain kolmogorov complexity two other interesting results are included first we prove that for any z 2 a 1 random real computable from a 1 z random real is automatically 1 z random second we give a plain kolmogorov complexity characterization of 1 randomness this characterization is related to our proof that x c y implies x vl y

modified cohen lee time frequency distributions and instantaneous bandwidth of multicomponent signals cohen 1989 1995 has introduced and extensively studied and developed the concept of the instantaneous bandwidth of a signal specifically instantaneous bandwidth is interpreted as the spread in frequency about the instantaneous frequency which is itself interpreted as the average frequency at each time this view stems from a joint time frequency distribution tfd analysis of the signal where instantaneous frequency and instantaneous bandwidth are taken to be the first two conditional spectral moments respectively of the distribution however the traditional definition of instantaneous frequency namely as the derivative of the phase of the signal is not consistent with this interpretation and new definitions have therefore been proposed previously we show that similar problems arise with the cohen lee 1988 1989 instantaneous bandwidth of a signal and propose a new formulation for the instantaneous bandwidth that is consistent with its interpretation as the conditional standard deviation in frequency of a tfd we give the kernel constraints for a distribution to yield this new result which is a modification of the kernel proposed by cohen and lee these new kernel constraints yield a modified cohen lee tfd whose first two conditional moments are interpretable as the average frequency and bandwidth at each time respectively

input output functions for stimulus frequency otoacoustic emissions in normal hearing adult ears input output i o functions for stimulus frequency sfoae and distortion product dpoae otoacoustic emissions were recorded in 30 normal hearing adult ears using a nonlinear residual method sfoaes were recorded at half octaves from 500 8000 hz in an l1 l2 paradigm with l2 0 to 85 db spl and in a paradigm with l1 fixed and l2 varied dpoaes were elicited with primary levels of kummer et al j acoust soc am 103 3431 3444 1998 at f2 frequencies of 2000 and 4000 hz interpretable sfoae responses were obtained from 1000 6000 hz in the equal level paradigm sfoae levels were larger than dpoaes levels signal to noise ratios were smaller and i o functions were less compressive a two slope model of sfoae i o functions predicted the low level round trip attenuation the breakpoint between linearity and compression and compressive slope in ear but not coupler recordings the noise at the sfoae frequency increased with increasing level above 60 db spl whereas noise at adjacent frequencies did no

what s next an interactive next best view approach shape from silhouettes algorithms use either a surface or a volumetric approach a problem with the volumetric approach is that in general we know neither the accuracy of the reconstruction nor where to locate new viewpoints for improving the accuracy in this paper we present a general approach to interactive object specific volumetric algorithms based on a necessary condition for the best possible reconstruction to have been performed the outlined approach can be applied to any class of objects as an example of this approach an interactive algorithm has been implemented for convex polyhedra

epipolar geometry from profiles under circular motion addresses the problem of motion estimation from profiles apparent contours of an object rotating on a turntable in front of a single camera a practical and accurate technique for solving this problem from profiles alone is developed it is precise enough to reconstruct the shape of the object no correspondences between points or lines are necessary symmetry of the surface of revolution swept out by the rotating object is exploited to obtain the image of the rotation axis and the homography relating epipolar lines in two views robustly and elegantly these together with geometric constraints for images of rotating objects are used to obtain first the image of the horizon which is the projection of the plane that contains the camera centers and then the epipoles thus fully determining the epipolar geometry of the image sequence the estimation of this geometry by this sequential approach avoids many of the problems found in other algorithms the search for the epipoles by far the most critical step is carried out as a simple 1d optimization parameter initialization is trivial and completely automatic at all stages after the estimation of the epipolar geometry the euclidean motion is recovered using the fixed intrinsic parameters of the camera obtained either from a calibration grid or from self calibration techniques finally the spinning object is reconstructed from its profiles using the motion estimated in the previous stage results from real data are presented demonstrating the efficiency and usefulness of the proposed methods

how far 3d shapes can be understood from 2d silhouettes each 2d silhouette of a 3d unknown object o constrains o inside the volume obtained by back projecting the silhouette from the corresponding viewpoint a set of silhouettes specifies a boundary volume r obtained by intersecting the volumes due to each silhouette r more or less closely approximates o depending on the viewpoints and the object itself this approach to the reconstruction of 3d objects is usually referred to as volume intersection this correspondence addresses the problem of inferring the shape of the unknown object o from the reconstructed object r for doing this the author divides the points of the surface of r into hard points which belong to the surface of any possible object originating r and soft points which may or may not belong to o the author considers two cases in the first case r is the closest approximation of o which can be obtained from its silhouettes i e its visual hull in the second case r is a generic reconstructed object in both cases the author supplies necessary and sufficient conditions for a point to be hard and gives rules for computing the hard surfaces

lower bounds on the redundancy in computations from random oracles via betting strategies with restricted wagers the kucera gacs theorem is a landmark result in algorithmic randomness asserting that every real is computable from a martin lof random real if the computation of the first n bits of a sequence requires n h n bits of the random oracle then h is the redundancy of the computation kucera implicitly achieved redundancy n log n while gacs used a more elaborate coding procedure which achieves redundancy n log n a similar bound is implicit in the later proof by merkle and mihailovic in this paper we obtain optimal strict lower bounds on the redundancy in computations from martin lof random oracles we show that any nondecreasing computable function g such that n 2 g n is not a general upper bound on the redundancy in computations from martin lof random oracles in fact there exists a real x such that the redundancy g of any computation of x from a martin lof random oracle satisfies n 2 g n moreover the class of such reals is comeager and includes a 2 0 real as well as all weakly 2 generic reals on the other hand it has been recently shown that any real is computable from a martin lof random oracle with redundancy g provided that g is a computable nondecreasing function such that n 2 g n hence our lower bound is optimal and excludes many slow growing functions such as log n from bounding the redundancy in computations from random oracles for a large class of reals our results are obtained as an application of a theory of effective betting strategies with restricted wagers which we develop

kolmogorov complexity of initial segments of sequences and arithmetical definability the structure of the k degrees provides a way to classify sets of natural numbers or infinite binary sequences with respect to the level of randomness of their initial segments in thek degrees of infinite binary sequences x is below y if the prefix free kolmogorov complexity of the first n bits of x is less than the complexity of the first n bits of y for each n identifying infinite binary sequences with subsets of n we study the k degrees of arithmetical sets and explore the interactions between arithmetical definability and prefix free kolmogorov complexity we show that in the k degrees for each n 1 there exists a s n 0 non zero degree which does not bound any d n 0 non zero degree an application of this result is that in the k degrees there exists a s 2 0 degree which forms a minimal pair with all s 1 0 degrees this extends the work of csima and montalban 2006 8 and merkle and stephan 2007 17 our main result is that given any d 2 0 family c of sequences there is a d 2 0 sequence of non trivial initial segment complexity which is not larger than the initial segment complexity of any non trivial member of c this general theorem has the following surprising consequence there is a 0 computable sequence of non trivial initial segment complexity which is not larger than the initial segment complexity of any non trivial computably enumerable set our analysis and results demonstrate that examining the extend to which arithmetical definability interacts with the k reducibility and in general any weak reducibility is a fruitful way of studying the induced structure

swept tone stimulus frequency otoacoustic emissions normative data and methodological considerations stimulus frequency otoacoustic emissions sfoaes are reflection source emissions and are the least familiar and perhaps most underutilized otoacoustic emission here normative sfoae data are presented from a large group of 48 young adults at probe levels from 20 to 60 db sound pressure level spl across a four octave frequency range to characterize the typical sfoae and describe recent methodological advances that have made its measurement more efficient in young adult ears sfoae levels peaked in the low to mid frequencies at mean levels of 6 7 db spl while signal to noise ranged from 23 to 34 db spl and test retest reliability was 4 db for 90 of the sfoae data on average females had 2 5 db higher sfoae levels than males sfoae input output functions showed near linear growth at low levels and a compression threshold averaging 35 db spl across frequency sfoae phase accumulated 32 36 cycles across four octaves on average and showed level effects when converted to group delay low level probes produced longer sfoae delays a break in the normalized sfoae delay was observed at 1 1 khz on average elucidating the location of the putative apical basal transition technical innovations such as the concurrent sweeping of multiple frequency segments post hoc suppressor decontamination and a post hoc artifact rejection technique were tested stimulus frequency otoacoustic emissions sfoaes are reflection source emissions and are the least familiar and perhaps most underutilized otoacoustic emission here normative sfoae data are presented from a large group of 48 young adults at probe levels from 20 to 60 db sound pressure level spl across a four octave frequency range to characterize the typical sfoae and describe recent methodological advances that have made its measurement more efficient in young adult ears sfoae levels peaked in the low to mid frequencies at mean levels of 6 7 db spl while signal to noise ranged from 23 to 34 db spl and test retest reliability was 4 db for 90 of the sfoae data on average females had 2 5 db higher sfoae levels than males sfoae input output functions showed near linear growth at low levels and a compression threshold averaging 35 db spl across frequency sfoae phase accumulated 32 36 cycles across four octaves on average and showed level effects when converted to group delay low level probe

distortion product otoacoustic emissions cochlear source contributions and clinical test performance it has been proposed that the clinical accuracy of distortion product otoacoustic emissions dpoaes is affected by the interaction of distortion and reflection sources contributing to the response this study evaluated changes in dichotomous decision test performance and threshold prediction accuracy when dpoae source contribution was controlled data were obtained from 205 normal and impaired ears with l2 ranging from 0 to 80db spl and f2 2 and 4khz data were collected for control conditions no suppressor f3 and with f3 presented at three levels that previously had been shown to reduce the reflection source contribution the results indicated that controlling source contribution with a suppressor did not improve diagnostic accuracy as reflected by relative operating characteristic curve area and frequently resulted in poorer test performance compared to control conditions likewise correlations between dpoae and behavioral thresholds were not strengthened when using the suppressors to control sou

on the frequency dependence of the otoacoustic emission latency in hypoacoustic and normal ears experimental measurements of the otoacoustic emission oae latency of adult subjects have been obtained as a function of frequency by means of wavelet time frequency analysis based on the iterative application of filter banks the results are in agreement with previous oae latency measurements by tognola et al hear res 106 112 122 1997 as regards both the latency values and the frequency dependence and seem to be incompatible with the steep 1 f law that is predicted by scale invariant full cochlear models the latency frequency relationship has been best fitted to a linear function of the cochlear physical distance using the greenwood map and to an exponential function of the cochlear distance for comparison with derived band abr latency measurements two sets of ears 94 audiometrically normal and 42 impaired with high frequency f 3 khz hearing loss have been separately analyzed significantly larger average latencies were found in the impaired ears in the mid frequency range theoreti

time frequency analysis of linear and nonlinear otoacoustic emissions and removal of a short latency stimulus artifact click evoked otoacoustic emissions ceoaes are commonly recorded as average responses to a repetitive click stimulus if the click train has constant polarity a linear average results if it contains a sequence of clicks of differing polarity and amplitude a nonlinear average can be calculated the purpose of this study was to record both protocols from the same set of ears and characterize the differences between them the major features of ceoaes were similar under both protocols with the exception of a region spanning 0 5 ms in time and 0 2 2 khz in frequency it was assumed that the signal derived from the linear protocol was contaminated by stimulus artifact and so a simple procedure was used involving high pass filtering and time windowing to remove components of this artifact this procedure preserved the short latency high frequency responses it also produced a marked similarity in the time frequency plots of recordings made under the two protocols this result means it is possible to take advantage of the better signal to noise ratio of the linear data compared to its nonlinear counterpart additionally it was shown that ceoaes recorded under the linear protocol appear to be less dependent on the presence of spontaneous otoacoustic emissions soaes

the visual hull of smooth curved objects the visual hull is a geometric entity that relates the shape of an object to its silhouettes or shadows this paper develops the theory of the visual hull of generic smooth objects we show that the visual hull can be constructed using surfaces which partition the viewpoint space of the aspect graph of the object the surfaces are those generated by the visual events tangent crossing and triple point an analysis based on the shape of the object at the tangency points of these surfaces allows pruning away many surfaces and patches not relevant to the construction an algorithm for computing the visual hull is outlined

computing exact aspect graphs of curved objects algebraic surfaces this article presents an algorithm for computing the exact aspect graph of an opaque solid bounded by a smooth algebraic surface orthographic projection is assumed the algorithm is based on a catalog of visual events available from singularity theory it uses curve tracing cell decomposition homotopy continuation and ray tracing to construct the regions of the view sphere delineated by visual event curves the algorithm has been fully implemented and examples are presented

on the number of infinite sequences with trivial initial segment complexity the sequences which have trivial prefix free initial segment complexity are known as k trivial sets and form a cumulative hierarchy of length w we show that the problem of finding the number of k trivial sets in the various levels of the hierarchy is d 3 0 this answers a question of downey miller yu see downey 2010 7 section 10 1 4 which also appears in nies 2009 17 problem 5 2 16 we also show the same for the hierarchy of the low for k sequences which are the ones that when used as oracles do not give a shorter initial segment complexity compared to the computable oracles in both cases the classification d 3 0 is sharp

the effects of neural synchronization and peripheral compression on the acoustic reflex threshold this study investigates the acoustic reflex threshold art dependency on stimulus phase utilizing low level reflex audiometry neumann et al audiol neuro otol 1 359 369 1996 the goal is to obtain optimal broadband stimuli for elicitation of the acoustic reflex and to obtain objective determinations of cochlear hearing loss three types of tone complexes with different phase characteristics were investigated a stimulus that compensates for basilar membrane dispersion thus causing a large overall neural synchrony basilar membrane tone complex bmtc the temporally inversed stimulus ibmtc and random phase tone complexes rtc the arts were measured in eight normal hearing and six hearing impaired subjects five different conditions of peak amplitude and stimulus repetition rate were used for each stimulus type the results of the present study suggest that the art is influenced by at least two different factors a the degree of synchrony of neural activity across frequency and b the fast acting compression mechanism in the cochlea that is reduced in the case of a sensorineural hearing loss the results allow a clear distinction of the two subjects groups based on the different art for the utilized types and conditions of the stimuli these differences might be useful for objective recruitment detection in clinical diagnostics

distortion product otoacoustic emission reflection component delays and cochlear tuning estimates from across the human lifespan a consistent relationship between reflection emission delay and cochlear tuning has been demonstrated in a variety of mammalian species as predicted by filter theory and models of otoacoustic emission oae generation as a step toward the goal of studying cochlear tuning throughout the human lifespan this paper exploits the relationship and explores two strategies for estimating delay trends energy weighting and peak picking both of which emphasize data at the peaks of the magnitude fine structure distortion product otoacoustic emissions dpoaes at 2f1 f2 were recorded and their reflection components were extracted in 184 subjects ranging in age from prematurely born neonates to elderly adults dpoaes were measured from 0 5 4 khz in all age groups and extended to 8 khz in young adults delay trends were effectively estimated using either energy weighting or peak picking with the former method yielding slightly shorter delays and the latter somewhat smaller confidence intervals delay and tuning est

real time object recognition in sparse range images using error surface embedding a novel object recognition algorithm is introduced to identify objects and recover their pose from sparse range data the method is based upon comparing the 7 d error surfaces of objects in various poses which result from the registration error function between two convolved surfaces the objects and their pose values are encoded by a small set of feature vectors extracted from the minima of the error surfaces the problem of object recognition is thus reduced to comparing these feature vectors to find the corresponding error surfaces between the runtime data and a preprocessed database the algorithm called potential well space embedding pwse has been implemented and tested on both simulated and real data the experimental results show the technique to be both effective and efficient executing at 122 frames per second on standard hardware and with recognition rates exceeding 97 for a database of 60 objects the performance of pwse on the large size database was also evaluated on the princeton shape benchmark containing 1 814 objects in addition it functions well with very sparse data possibly comprising only hundreds of points per image and is shown to be robust to measurement error and outliers with some small modifications we applied pwse to the problem of object class recognition in experiments with the princeton shape benchmark pwse is able to provides better classification rates than the previous methods in terms of nearest neighbour classification

the scale space aspect graph currently the aspect graph is computed from the theoretical standpoint of perfect resolution in object shape the viewpoint and the projected image this means that the aspect graph may include details that an observer could never see in practice introducing the notion of scale into the aspect graph framework provides a mechanism for selecting a level of detail that is large enough to merit explicit representation this effectively allows control over the number of nodes retained in the aspect graph this paper introduces the concept of the scale space aspect graph defines three different interpretations of the scale dimension and presents a detailed example for a simple class of objects with scale defined in terms of the spatial extent of features in the image

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

instantaneous spectral bandwidth and dominant frequency with applications to seismic reflection data fourier power spectra are often usefully characterized by average measures in reflection seismology the important average measures are center frequency spectral bandwidth and dominant frequency these quantities have definitions familiar from probability theory center frequency is the spectral mean spectral bandwidth is the standard deviation about that mean and dominant frequency is the square root of the second moment which serves as an estimate of the zero crossing frequency these measures suggest counterparts defined with instantaneous power spectra in place of fourier power spectra so that they are instantaneous in time though they represent averages in frequency intuitively reasonable requirements yield specific forms for these instantaneous quantities that can be computed with familiar complex seismic trace attributes instantaneous center frequency is just instantaneous frequency instantaneous bandwidth is the absolute value of the derivative of the instantaneous amplitude divided by t

distortion product otoacoustic emission generation mechanisms and their dependence on stimulus level and primary frequency ratio in this study a systematic analysis of the dependence on stimulus level and primary frequency ratio r of the different components of human distortion product otoacoustic emissions has been performed to check the validity of theoretical models of their generation as regards the localization of the sources and the relative weight of distortion and reflection generation mechanisms 2f1 f2 and 2f2 f1 distortion product otoacoustic emissions of 12 normal hearing ears from six human subjects have been measured at four different levels in the range 35 65 db sound pressure level at eight different ratios in the range 1 1 1 45 time frequency filtering was used to separate distortion and reflection components numerical simulations have also been performed using an active nonlinear cochlear model both in the experiment and in the simulations the behavior of the 2f1 f2 distortion and reflection components was in agreement with previous measurements and with the predictions of the two source model the 2f2 f1 response showed a rotating phase component only whose behavior was in general agreement with that predicted for a component generated and reflected within a region basal to the characteristic place of frequency 2f2 f1 although alternative interpretations which are also discussed cannot be ruled out

lowness properties and randomness abstract the set a is low for martin lof randomness if each random set is already random relative to a a is k trivial if the prefix complexity k of each initial segment of a is minimal namely n k a n k n o 1 we show that these classes coincide this answers a question of ambos spies and kucera in p cholak s lempp m lerman r shore eds computability theory and its applications current trends and open problems american mathematical society providence ri 2000 each low for martin lof random set is 2 0 our class induces a natural intermediate 3 0 ideal in the r e turing degrees which generates the whole class under downward closure answering a further question in p cholak s lempp m lerman r shore eds computability theory and its applications current trends and open problems american mathematical society providence ri 2000 we prove that each low for computably random set is computable

wavelet and matching pursuit estimates of the transient evoked otoacoustic emission latency different time frequency techniques may be used to investigate the relation between latency and frequency of transient evoked otoacoustic emissions in this work the optimization of these techniques and the interpretation of the experimental result are discussed time frequency analysis of click evoked otoacoustic emissions of 42 normal hearing young subjects has been performed using both wavelet and matching pursuit algorithms wavelet techniques are very effective to provide fast and reliable evaluation of the average latency of large samples of subjects a major advantage of the matching pursuit technique as observed by jedrzejczak et al j acoust soc am 115 2148 2158 2004 is to provide detailed information about the time evolution of the response of single ears at selected frequencies a hybrid matching pursuit algorithm that includes fourier spectral information was developed capable of speeding up computation times and of identifying spurious atoms whose latency frequency relation i

sources of distortion product otoacoustic emissions revealed by suppression experiments and inverse fast fourier transforms in normal ears primary and secondary sources combine to produce the 2f1 f2 distortion product otoacoustic emission dpoae measured in the ear canals of humans dpoaes were obtained in nine normal hearing subjects using a fixed f2 paradigm in which f1 was varied the f2 was 2 or 4 khz and absolute and relative primary levels were varied data were obtained with and without a third tone f3 placed 15 6 hz below 2f1 f2 the level of f3 was varied in order to suppress the stimulus frequency otoacoustic emission sfoae coming from the 2f1 f2 place these data were converted from the complex frequency domain into an equivalent time representation using an inverse fast fourier transform ifft iffts of unsuppressed dpoae data were characterized by two or more peaks relative amplitudes of these peaks depended on overall primary level and on primary level differences the suppressor eliminated later peaks but early peaks remained relatively unaltered results are interpreted to mean that the dpoae measured in humans includes components from the f2 place intermodulation distortion and dp place in the form of a sfoae these findings build on previous work by providing evidence that multiple peaks in the ifft are due to a secondary source at the dp place

projective visual hulls this article presents a novel method for computing the visual hull of a solid bounded by a smooth surface and observed by a finite set of cameras the visual hull is the intersection of the visual cones formed by back projecting the silhouettes found in the corresponding images we characterize its surface as a generalized polyhedron whose faces are visual cone patches edges are intersection curves between two viewing cones and vertices are frontier points where the intersection of two cones is singular or intersection points where triples of cones meet we use the mathematical framework of oriented projective differential geometry to develop an image based algorithm for computing the visual hull this algorithm works in a weakly calibrated setting that is it only requires projective camera matrices or equivalently fundamental matrices for each pair of cameras the promise of the proposed algorithm is demonstrated with experiments on several challenging data sets and a comparison to another state of the art method

computing the discrete time analytic signal via fft starting with a real valued n point discrete time signal frequency domain algorithms are provided for computing 1 the complex valued standard n point discrete time analytic signal of the same sample rate 2 the complex valued decimated n 2 point discrete time analytic signal of half the original sample rate and 3 the complex valued interpolated nm point discrete time analytic signal of m times the original sample rate special adjustment of the transform end points are shown to be necessary in order to generate proper discrete time analytic signals

comparing the optimal signal conditions for recording cubic and quadratic distortion product otoacoustic emissions odd and even order distortion products dps evoked by two primary tones f1 f2 f1 f2 represent different aspects of cochlear nonlinearity the cubic and quadratic difference tones cdt 2f1 f2 and qdt f2 f1 are prominent representatives of the odd and even dps distortion product otoacoustic emissions dpoaes were measured within a primary level l1 l2 space over a wide range of f2 f1 ratios to compare the optimal signal conditions for these dps for cdt the primary level difference decreased as l1 increased with a rate proportional to the f2 f1 ratio moreover the optimal ratio increased with l1 a set of two formulas is proposed to describe the optimal signal conditions however for a given level of a primary increasing the other tone level could maximize the qdt amplitude the frequency ratio at the maximal qdt was about 1 3 and quite constant across different primary levels a notch was found in the qdt amplitude at the f2 f1 ratio of about 1 22 1 25 these opposite behaviors suggest that the optimal recording conditions are different for cdt and qdt due to the different aspects in the cochlear nonlinearity optimizing the dpoae recordings could improve the reliability in clinical or research practices

oscillation in the initial segment complexity of random reals abstract we study oscillation in the prefix free complexity of initial segments of 1 random reals for upward oscillations we prove that n 2 g n diverges iff n k x n n g n for every 1 random x 2 for downward oscillations we characterize the functions g such that n k x n n g n for almost every x 2 the proof of this result uses an improvement of chaitin s counting theorem we give a tight upper bound on the number of strings 2 n such that k n k n m the work on upward oscillations has applications to the k degrees write x k y to mean that k x n k y n o 1 the induced structure is called the k degrees we prove that there are comparable 2 0 1 random k degrees we also prove that every lower cone and some upper cones in the 1 random k degrees have size continuum finally we show that it is independent of zfc even assuming that the continuum hypothesis fails whether all chains of 1 random k degrees of size less than 2 0 have a lower bound in the 1 random k degrees

computing the generalized aspect graph for objects with moving parts algorithms for computing the aspect graph representation are generalized to include a larger more realistic domain of objects known as articulated assemblies those objects composed of rigid parts with articulated connections allowed between parts the generalization suggests two slightly different representations one that directly summarizes the possible general views of the object and another hierarchical form summarizing the possible general configurations and their respective views algorithms are outlined for computing both representations the generalized aspect graphs of assemblies formed using translational connections are examined

evidence for the distortion product frequency place as a source of distortion product otoacoustic emission dpoae fine structure in humans ii fine structure for different shapes of cochlear hearing loss distortion product otoacoustic emissions dpoae were recorded from eight human subjects with mild to moderate cochlear hearing loss using a frequency spacing of 48 primary pairs per octave and at a level l1 l2 60 dbspl and with a fixed ratio f2 f1 subjects with different shapes of hearing thresholds were selected they included subjects with near normal hearing within only a limited frequency range subjects with a notch in the audiogram and subjects with a mild to moderate high frequency loss if the primaries were located in a region of normal or near normal hearing but dp frequencies were located in a region of raised thresholds the distortion product 2 f1 f2 was still observable but the dp fine structure disappeared if the dp frequencies fell into a region of normal thresholds fine structure was preserved as long as dpoae were generated even in cases of mild hearing loss in the region of the primaries these experimental results give further strong evidence that in addition to the initial s

level dependence of the nonlinear distortion component of distortion product otoacoustic emissions in humans distortion product otoacoustic emissions dpoaes emerge when presenting two primary tones with different frequencies f1 and f2 to the cochlea and are commonly used in diagnosis and research to evaluate the functional state of the cochlea optimal primary tone stimulus levels accounting for the different level dependencies of the traveling wave amplitudes of the two primary tones near the f2 tonotopic place on the basilar membrane are often used to maximize dpoae amplitudes however parameters defining the optimal levels can be affected by wave interference between the nonlinear distortion and coherent reflection components of the dpoae here the components were separated in the time domain using a pulsed stimulus paradigm and optimal levels determined based on the amplitude dependence of the nonlinear distortion components on primary tone stimulus levels level parameters yielding maximum dpoae amplitudes were derived for six normal hearing adults and compared to data recorded with continuous two tone stimulation the level parameters resulting from analysis of the nonlinear distortion components show dependence on stimulus frequency and small standard deviations dpoae input output functions derived for optimal levels exhibit larger slopes wider dynamic range and less variability across subjects than those derived for conventional stimulus and analysis conditions potentially increasing their reliability and sensitivity for assessing cochlea function

influence of primary level and primary frequency ratios on human distortion product otoacoustic emissions the combined influence of primary level differences l1 l2 and primary frequency ratio f2 f1 on distortion product otoacoustic emission dpoae level was investigated in 20 normal hearing subjects dpoaes were recorded with continuously varying stimulus levels neely et al j acoust soc am 117 1248 1259 2005 for the following stimulus conditions f2 1 2 4 and 8 khz and f2 f1 1 05 to 1 4 various l1 l2 including one individually optimized to produce the largest dpoae for broadly spaced primary frequencies at low l2 levels the largest dpoaes were recorded when l1 was much higher than l2 with l1 remaining relatively constant as l2 increased as f2 fl decreased the largest dpoaes were observed when l1 was closer to l2 and increased as l2 increased optimal values for l1 l2 and f2 f1 were derived from these data in general average dpoae levels for the new l1 l2 and f2 f1 were equivalent to or larger than those observed for other stimulus combinations including the l1 l2 described by kummer et al j acoust soc am 103 3431 3444 1998 and those defined by neely et al in which l1 l2 was evaluated but f2 f1 was fixed at 1 2

input output functions of the nonlinear distortion component of distortion product otoacoustic emissions in normal and hearing impaired human ears distortion product otoacoustic emissions dpoaes arise in the cochlea in response to two tones with frequencies f1 and f2 and mainly consist of two components a nonlinear distortion and a coherent reflection component wave interference between these components limits the accuracy of dpoaes when evaluating the function of the cochlea with conventional continuous stimulus tones here dpoae components are separated in the time domain from dpoae signals elicited with short stimulus pulses the extracted nonlinear distortion components are used to derive estimated distortion product thresholds edpts from semi logarithmic input output i o functions for 20 normal hearing and 21 hearing impaired subjects i o functions were measured with frequency specific stimulus levels at eight frequencies f2 1 8 khz f2 f1 1 2 for comparison dpoaes were also elicited with continuous primary tones both acquisition paradigms yielded edpts which significantly correlated with behavioral thresholds p 0 001

acquiring 3 d models from sequences of contours this paper explores shape from contour for acquiring 3 d graphics models in this method a continuous sequence of images is taken as an object rotates a smooth convex shape can be estimated instantaneously from its contour and by the first derivative of contour movement trace of contour or contour distribution with time we also analyze shapes that do not satisfy the conditions of smoothness and visibility which are indispensable for modeling an object a region that does not expose as contour yields a nonsmoothness in the tracked contour movement we can thus detect such a region by contour distribution filtering and extract its accurate location by computing the left and right derivatives of the distribution this has not been studied previously these unknown regions are obtained for further investigation using other visual cues a general approach for building a geometrical object model using contours is then described the entire process from silhouettes to a 3 d model is based local computation this is promising for producing shapes in real time our direct goal is to establish 3 d graphics models of human faces for the growing needs of visual communications we have obtained some good results

efficiently computing and representing aspect graphs of polyhedral objects an efficient algorithm and a data structure for computing and representing the aspect graph of polyhedral objects under orthographic projection are presented the aspect graph is an approach to representing 3 d objects by a set of 2 d views for the purpose of object recognition in this approach the viewpoint space is partitioned into regions such that in each region the qualitative structure of the line drawing does not change the viewing data of an object is the partition of the viewpoint space together with a representative view in each region the algorithm computes the viewing data for line drawings of polyhedral objects under orthographic projection

the geometry of view space of opaque objects bounded by smooth surfaces abstract a view of a smooth opaque object is a line drawing consisting of contour fragments which form closed loops terminate or form t junctions given a compact object we have a global decomposition of the space of camera positions into cells from which topologically equivalent views are obtained to apply certain image based object recognition techniques based on characteristic views of an object one needs to know this cellular decomposition of view space the boundaries of such cells of stable views are formed by the view bifurcation set from which transitional degenerate views are seen we derive a finite list of geometrical models of the view bifurcation set the view bifurcation set of any particular object is a combination of such model surfaces from this list to match a characteristic view with an image one has to find the visible fragments of the apparent contour in the image and we briefly describe an observation which might lead to an algorithm for finding such contour fragments

the enumerative geometry of projective algebraic surfaces and the complexity of aspect graphs the aspect graph is a popular viewer centered representation that enumerates all the topologically distinct views of an object building the aspect graph requires partitioning viewpoint space in view equivalent cells by a certain number of visual event surfaces if the object is piecewise smooth algebraic then all visual event surfaces are either made of lines having specified contacts with the object or made of lines supporting the points of contacts of planes having specified contacts with the object in this paper we present a general framework for studying the enumerative properties of line and plane systems the context is that of enumerative geometry and intersection theory in particular we give exact results for the degrees of all visual event surfaces coming up in the construction of aspect graphs of piecewise smooth algebraic bodies we conclude by giving a bound on the number of topologically distinet views of such objects

moments of click evoked otoacoustic emissions in human ears group delay and spread instantaneous frequency and bandwidth a click evoked otoacoustic emission ceoae has group delay and spread as first and second order temporal moments varying over frequency and instantaneous frequency and bandwidth as first and second order spectral moments varying over time energy smoothed moments were calculated from a ceoae database over 0 5 15 khz bandwidth and 0 25 20 ms duration group delay and instantaneous frequency were calculated without phase unwrapping using a coherence synchrony measure that accurately classified ears with hearing loss ceoae moment measurements were repeatable in individual ears group delays were similar for ceoaes and stimulus frequency oaes group spread is a frequency specific measure of temporal spread in an emission related to spatial spread across tonotopic generation sites along the cochlea in normal ears group delay and spread increased with frequency and decreased with level a direct measure of cochlear tuning above 4 khz was analyzed using instantaneous frequency and bandwidth synchronized spontaneous oaes were present in most ears below 4 khz and confounded interpretation of moments in ears with sensorineural hearing loss group delay and spread varied with audiometric classification and amount of hearing loss group delay differed between older males and females ceoae moments reveal clinically relevant information on cochlear tuning in ears with normal and impaired hearing

sources of dpoaes revealed by suppression experiments inverse fast fourier transforms and sfoaes in impaired ears dpoae sources are modeled by intermodulation distortion generated near the f2 place and a reflection of this distortion near the dp place in a previous paper inverse fast fourier transforms iffts of dpoae filter functions in normal ears were consistent with this model konrad martin et al j acoust soc am 109 2862 2879 2001 in the present article similar measurements were made in ears with specific hearing loss configurations it was hypothesized that hearing loss at f2 or dp frequencies would influence the relative contributions to the dpoae from the corresponding basilar membrane places and would affect the relative magnitudes of sfoaes at frequencies equal to f2 and fdp dpoaes were measured with f2 4 khz f1 varied and a suppressor near fdp l2 was 25 55 db spl l1 l2 10 db sfoaes were measured at f2 and at 2 7 khz the average fdp produced by the f1 sweep for stimulus levels of 20 60 db spl sfoae results supported predictions of the pattern of amplitude differences between sfoaes

characteristics of the 2f1 f2 distortion product otoacoustic emission in a normal hearing population distortion product otoacoustic emission dpoae fine structure and component characteristics are reported between 0 75 and 16 khz in 356 clinically normal hearing human subjects ages 10 to 65 yr stimulus tones at 55 40 65 55 and 75 75 db spl were delivered using custom designed drivers and a calibration method that compensated for the depth of insertion of the otoacoustic emission oae probe in the ear canal dpoae fine structure depth and spacing were found to be consistent with previous reports with depth varying between 3 and 7 db and average spacing ratios f f between 15 and 25 depending on stimulus level and frequency in general fine structure depth increased with increasing frequency likely due to a diminishing difference between dpoae component levels fine structure spacing became wider with increasing age above 8 khz dpoae components were extracted using the inverse fast fourier transform method adhering to a strict signal to noise ratio criterion for clearer interpretation component data from four age groups between 18 and 55 yr old were available for the stimulus levels of 75 75 db spl the age groups could be differentiated with greater than 90 accuracy when using the level of the component presumed to originate from the dpoae characteristic frequency place this accuracy held even for frequencies at and below 4 khz where the age groups exhibited similar average hearing thresholds

time domain demonstration of distributed distortion product otoacoustic emission components distortion product otoacoustic emissions dpoaes were measured in rabbits as time waveforms by employing a phase rotation technique to cancel all components in the final average except the 2f1 f2 dpoae subsequent filtering allowed the dpoae waveform to be clearly visualized in the time domain in most conditions f2 was turned off for 6 ms which produced a gap so that the dpoae was no longer generated these procedures allowed the dpoae onset as well as the decay during the gap to be observed in the time domain dpoaes were collected with l1 l2 65 db sound pressure level primary tone levels for f2 f1 ratios from 1 25 to 1 01 in 0 02 steps findings included the appearance of complex onsets and decays for the dpoae time waveforms as the f2 f1 ratio was decreased and the dpoae level was reduced these complexities were unaffected by interference tones its near the dpoae frequency place fdp but could be removed by its presented above f2 which also increased dpoae levels similar outcomes were o

the visual hull concept for silhouette based image understanding many algorithms for both identifying and reconstructing a 3 d object are based on the 2 d silhouettes of the object in general identifying a nonconvex object using a silhouette based approach implies neglecting some features of its surface as identification clues the same features cannot be reconstructed by volume intersection techniques using multiple silhouettes of the object this paper addresses the problem of finding which parts of a nonconvex object are relevant for silhouette based image understanding for this purpose the geometric concept of visual hull of a 3 d object is introduced this is the closest approximation of object s that can be obtained with the volume intersection approach it is the maximal object silhouette equivalent to s i e which can be substituted for s without affecting any silhouette only the parts of the surface of s that also lie on the surface of the visual hull can be reconstructed or identified using silhouette based algorithms the visual hull depends not only on the object but also on the region allowed to the viewpoint two main viewing regions result in the external and internal visual hull in the former case the viewing region is related to the convex hull of s in the latter it is bounded by s the internal visual hull also admits an interpretation not related to silhouettes algorithms for computing visual hulls are presented and their complexity analyzed in general the visual hull of a 3 d planar face object turns out to be bounded by planar and curved patches

the bootstrap and modern statistics 2000 the bootstrap and modern statistics journal of the american statistical association vol 95 no 452 pp 1293 1296

time frequency domain filtering of evoked otoacoustic emissions time domain filtering is a standard analysis technique which is used to disentangle the two main vector components of the distortion product otoacoustic emission response exploiting their different phase frequency relation in this study a time frequency filtering technique based on the continuous wavelet transform is proposed to overcome the intrinsic limitations of the time domain filtering technique and to extend it also to the analysis of stimulus frequency and transient evoked otoacoustic emissions the advantages of the proposed technique are first discussed on a theoretical basis then practically demonstrated by applying it to the analysis of synthesized and real otoacoustic data the results show that the time frequency approach can be empirically optimized to get effective separation of the components of the otoacoustic response associated with either different generation mechanisms or different generation places focusing on a single component of the otoacoustic response with a given time frequency signature may also improve significantly the signal to noise ratio because the random noise contribution tends to be uniformly distributed on the time frequency plane

chaitin s halting probability and the compression of strings using oracles if a computer is given access to an oracle the characteristic function of a set whose membership relation may or may not be algorithmically calculable this may dramatically affect its ability to compress information and to determine structure in strings which might otherwise appear random this leads to the basic question given an oracle a how many oracles can compress information at most as well as a this question can be formalized using kolmogorov complexity we say that b lka if there exists a constant c such that ka kb c for all strings where kx denotes the prefix free kolmogorov complexity relative to oracle x the formal counterpart to the previous question now is what is the cardinality of the set of lk predecessors of a we completely determine the number of oracles that compress at most as well as any given oracle a by answering a question of miller notre dame j formal logic 2010 50 381 391 which also appears in nies computability and randomness oxford uk oxford university press 2009 problem 8 1 13 the class of lk predecessors of a set a is countable if and only if chaitin s halting probability is martin lof random relative to a

identification of otoacoustic emissions components by means of adaptive approximations clicks and a set of tone bursts covering the same frequency band were applied as a stimuli evoking otoacoustic emissions oae recorded otoacoustic emissions were decomposed into the basic waveforms by means of high resolution adaptive time frequency approximation method based on the matching pursuit algorithm the method allows for description of the signal components in terms of frequencies time occurrences time spans and energy the analysis of oae s energy density distributions in time frequency space revealed that click responses can be considered as linear superpositions of responses to tone bursts the frequency latency relationship was studied and compared with earlier works the method made possible the exhaustive description of the resonant modes specific for given subject ear they were characterized not only by the close frequencies appearing for different tones but they usually had similar latencies and time spans short time and long time resonant modes were identified the second ones