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Efficacy and safety of a hyaluronic acid filler in subjects treated for correction of midface volume deficiency: a 24 month study
Callan P,Goodman GJ,Carlisle I,Liew S
Clinical, Cosmetic and Investigational Dermatology , 2013,

Abstract: Peter Callan,1 Greg J Goodman,2 Ian Carlisle,3 Steven Liew,4 Peter Muzikants,5 Terrence Scamp,6 Michael B Halstead,7 John D Rogers71Peter Callan Plastic Surgery, Geelong, VIC, 2Dermatology Institute of Victoria, South Yarra, VIC, 3Erase Skin Rejuvenation Specialists, Malvern, VIC, 4Shape Clinic and Medispa, Darlinghurst, NSW, 5Ada Cosmetic Medicine, Glebe, NSW, 6Esteem Beauty and Day Spa, Main Beach, QLD, 7Allergan Medical Affairs, Gordon, ACT, AustraliaBackground: Hyaluronic acid (HA) fillers are an established intervention for correcting facial volume deficiency. Few studies have evaluated treatment outcomes for longer than 6 months. The purpose of this study was to determine the durability of an HA filler in the correction of midface volume deficiency over 24 months, as independently evaluated by physician investigators and subjects.Methods: Subjects received treatment with Juvéderm Voluma to the malar area, based on the investigators' determination of baseline severity and aesthetic goals. The treatment was administered in one or two sessions over an initial 4-week period. Supplementary treatment was permissible at week 78, based on protocol-defined criteria. A clinically meaningful response was predefined as at least a one-point improvement on the MidFace Volume Deficit Scale (MFVDS) and on the Global Aesthetic Improvement Scale (GAIS).Results: Of the 103 subjects enrolled, 84% had moderate or significant volume deficiency at baseline. At the first post-treatment evaluation (week 8), 96% were documented to be MFVDS responders, with 98% and 100% graded as GAIS responders when assessed by the subjects and investigators, respectively. At week 78, 81.7% of subjects were still MFVDS responders, with 73.2% and 78.1% being GAIS responders, respectively. Seventy-two subjects completed the 24-month study, of whom 45 did not receive supplementary Voluma at week 78. Forty-three of the 45 (95.6%) subjects were MFVDS responders, with 82.2% and 91.1% being GAIS responders, respectively. At end of the study, 66/72 subjects were either satisfied or very satisfied with Voluma , with 70/72 indicating that they would recommend the product to others. Adverse events were transient and infrequent, with injection site bruising and swelling being the most commonly reported.Conclusion: Voluma is safe and effective in the correction of mild to severe facial volume deficiency, achieving long-term clinically meaningful results. There was a high degree of satisfaction with the treatment outcome over the 24 months of the study.Keywords: hyaluronic acid, dermal fillers, volu

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Field Theories for Learning Probability Distributions
William Bialek,Curtis G. Callan,S. P. Strong
Physics , 1996, DOI: 10.1103/PhysRevLett.77.4693

Abstract: Imagine being shown $N$ samples of random variables drawn independently from the same distribution. What can you say about the distribution? In general, of course, the answer is nothing, unless we have some prior notions about what to expect. From a Bayesian point of view we need an {\it a priori} distribution on the space of possible probability distributions, which defines a scalar field theory. In one dimension, free field theory with a constraint provides a tractable formulation of the problem, and we also discus generalizations to higher dimensions.

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A Determinant of Stirling Cycle Numbers Counts Unlabeled Acyclic Single-Source Automata
David Callan
Discrete Mathematics & Theoretical Computer Science , 2008,

Abstract: We show that a determinant of Stirling cycle numbers counts unlabeled acyclic single-source automata. The proof involves a bijection from these automata to certain marked lattice paths and a sign-reversing involution to evaluate the determinant. We also give a formula for the number of acyclic automata with a given set of sources.

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Two Bijections for Dyck Path Parameters
David Callan
Mathematics , 2004,

Abstract: Here we give two bijections, one to show that the number of UUU-free Dyck n-paths is the Motzkin number M_n, the other to obtain the (known) distributions of the parameters "number of UDUs" and "number of DDUs" on Dyck n-paths. The first bijection is straightforward, the second not quite so obvious.

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Some bijections for restricted Motzkin paths
David Callan
Mathematics , 2004,

Abstract: We give several bijections among restricted Motzkin paths, explaining why various parameters on these paths are equidistributed. For example, the number of doublerise-free Motzkin paths of length n is the same as the number of peak-free Motzkin paths of length n+1 and the parameter "number of doublefalls" has the same distribution on the former set as "number of valleys" does on the latter. The bijections are most easily presented recursively but we also give explicit descriptions using the notion of Motzkin tree.

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A combinatorial proof of Sun's "curious" identity
David Callan
Mathematics , 2004,

Abstract: A binomial coefficient identity due to Zhi-Wei Sun is the subject of half a dozen recent papers that prove it by various analytic techniques and establish a generalization. Here we give a simple proof that uses weight-reversing involutions on suitable configurations involving dominos and colorings. With somewhat more work, the method extends to the generalization also.

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A combinatorial derivation of the number of labeled forests
David Callan
Mathematics , 2003,

Abstract: Lajos Takacs gave a somewhat formidable alternating sum formula for the number of forests of unrooted trees on $n$ labeled vertices. Here we use a weight-reversing involution on suitable tree configurations to give a combinatorial derivation of Takacs' formula.

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A Wilf equivalence related to two stack sortable permutations
David Callan
Mathematics , 2005,

Abstract: A permutation is so-called two stack sortable if it (i) avoids the (scattered) pattern 2-3-4-1, and (ii) contains a 3-2-4-1 pattern only as part of a 3-5-2-4-1 pattern. Here we show that the permutations on [n] satisfying condition (ii) alone are equinumerous with the permutations on [n] that avoid the mixed scattered/consecutive pattern 31-4-2. The proof uses a known bijection from 3-2-1-avoiding to 3-1-2-avoiding permutations.

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Some identities for the Catalan and Fine numbers
David Callan
Mathematics , 2005,

Abstract: We establish combinatorial interpretations of several identities for the Catalan and Fine numbers and, along the way, we present some new bijections of independent interest. Briefly, we show that C_{n} = 1/(n+1) Sum_{k} (n+1)choose(2k+1) (n+k)choose(k) counts ordered trees on n edges by number of interior vertices adjacent to a leaf, and C_{n} = 2/(n+1) Sum_{k} (n+1)choose(k+2) (n-2)choose(k) counts Dyck n-paths by number of long interior inclines. We also give an analogue for the Fine numbers of Touchard's Catalan number identity.

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