Background:  The "zipper model of empathy" has been proposed for psychopathy. It postulates that empathic behavior may fail to arise due to impaired facial emotion recognition. In this study, we examined if the model may be of relevance for schizophrenia.

Conclusions:  Our results suggest that the "zipper model of empathy" may be relevant for schizophrenia. The findings further point to the potential benefit of including social cognitive training in the treatment of persons with schizophrenia and a history of interpersonal aggression.


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Physics students the world over encounter the zipper problem at some point in their studies. It is a simple statistical physics model of the formation or unraveling of a long chain of links (often used as a toy model for DNA). Part of the reason that the zipper problem is so popular in homework assignments is that it has a great balance of interesting physics with relatively simple calculations.

The first step to solving any Maxwell-Boltzmann statistics problem is calculating the partition function. This is surprisingly easy for our single-ended zipper. Recall that a partition function is defined by the following sum:

In the equations above, we are summing to (N-1), not N. This is because we assume that the last link of the zipper will never be open (i.e. the two halves of the zipper can never disconnect and drift apart). Since \(\epsilon\), \(k\), and \(T\) are all positive, the exponent will always be less than or equal to one. Thus, we can turn to the geometric series to simplify the expression. Recall that:

Once you determine the partition function, you can solve for any number of thermodynamic quantities. Traditionally, one is asked to solve for the average number of open links on the zipper \(\langle s \rangle\). This is just the sum over all states of the probability of being in that state (P) multiplied by the index of the state (s):

Not quite little cupcake. It is true that \(exp(-\beta\epsilon)\) can never equal one, so we will never see a phase transition in the traditional solution to the zipper problem where \(G=1\). However, the expression \(x = Gexp(-\beta \epsilon)\) can equal one if G is large enough.

To represent DNA replication using a twisted zipper model, a second zipper track parallel to the original track can be introduced to demonstrate the semiconservative nature of DNA replication. However, this model has limitations in representing the complexity of the actual replication process.

To represent DNA replication in eukaryotes using a twisted zipper model, one could introduce a second zipper track parallel to the original one and show how each zipper track unzips and forms two new complementary strands. This would demonstrate the semiconservative nature of DNA replication, where each new DNA molecule contains one original strand and one newly synthesized strand. However, the twisted zipper model has limitations in representing the complex process of DNA replication, such as the involvement of multiple enzymes and the bidirectional nature of replication.

The model of the DNA can be related to a zipper. Just like the zipper, the two strands of the DNA are joined together by the hydrogen bonds present between the nucleotides. At the time of replication, the coiling of the two strands is undone just as the zipper is open. The two strands of the DNA open and separate just as the two stands of the zipper open and separate. Each strand can give rise to anew strand.

Carl Goldberg's Zipper has been said to be the world's best known free flight model. An unforgettable aircraft that revolutionized the world of free flight in the 1930's with its performance and features. Most notable was the pylon mounted wing producing a natural corkscrew climb. Introduced in the June 1939 Model Airplane News as a Comet Model Airplane Company kit, It was reported that over 700 Zippers were entered in the 1939 Nationals. The original Zipper with a 54" span and 488 sq.in. area, with a Dennymite .57 ignition engine,weighed between 26-36 producing a wing loading of 7 to 10  oz/sq ft depending on the battery and coil used; right in line with the SAM Texaco 8 oz/sq ft rule. The BMJR Zipper with a 44" span and 333 sq. in. area with a flying weight of 18.5 oz for 8oz/sf wing loading for either 1/2A or electric Texaco. Recomended power is the Cox Texaco .049 or the geared Speed 400 (S-400). Withe the electric power and speed control we have found this to be our favorite sport flyer.

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You could use the ShrinkWrap modifier to lay the curve on the boot mesh, then have the zipper follow the curve.

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Here is my quick build. Find good flat image of zipper assembly for background image. Build your model from this template; pic A, slider build and pic B, teeth. Slider has mirror modifier on it, so that only one side needs to be built. All teethes are identical so you only need to build one teeth object. Assemble it with Array modifier, to add row of teethes. Now add Curve modifier to bend the zip line. Duplicate the other side of zip line and offset it, so that teeth fit at the joined bottom. I found zip line bends sharply as slider slides over them. Gentle curve bend will not do. You can probably getaway with straight curve with hard bend on it.

Multi functional pencil case for writing utensils, lockable with a zipper. Handy case can also be used standing up on your desk. This compact case fits perfectly with all items in our range, so you can put together a nice set. The stylish and authentic Italian leather is the hallmark of Tony Perotti and is produced in an environmentally friendly process.

The FlipBelt Zipper running belt enhances the security of the classic FlipBelt by featuring an extra secure zipper pocket in the travel belt pouch you already love to use. FlipBelt Zipper running belt is also the perfect security travel belt and designed to accommodate passports while traveling and holds extra-large phones, such as the iPhone 12 Pro Max and Samsung Galaxy S21 Ultra. (Phone Compatibility List)

The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems. Today, Lee-Yang zeros are no longer just a theoretical concept; they have been determined in recent experiments. In one approach, the Lee-Yang zeros are extracted from the high cumulants of thermodynamic observables at finite size. Here we employ this method to investigate a phase transition in a molecular zipper. From the energy fluctuations in small zippers, we can predict the temperature at which a phase transition occurs in the thermodynamic limit. Even when the system does not undergo a sharp transition, the Lee-Yang zeros carry important information about the large-deviation statistics and its symmetry properties. Our work suggests an interesting duality between fluctuations in small systems and their phase behavior in the thermodynamic limit. These predictions may be tested in future experiments.

Zipper model, Lee-Yang zeros, and large-deviation statistics. (a) The molecular zipper is a double-stranded macromolecule held together by N links that can be either open (energy ) or closed (energy 0). At the transition temperature Tc, the system goes through a phase transition. (b) Lee-Yang zeros in the complex plane of the inverse temperature =1/kBT. (c) Large-deviation statistics of the energy per link for large N. Distributions are shown for three different temperatures =0.7c,c,1.3c, with c=1/kBTc.

Free energy of the molecular zipper. (a) Free energy per link as a function of the temperature T for different numbers of open links n=0,1,...,N. For TTc, the open zipper has the lowest free energy. The equilibrium free energy is shown with a thick black line. (b) Equilibrium free energy per link for different lengths of the zipper. In the thermodynamic limit, the equilibrium free energy per link becomes nonanalytic at T=Tc.

Average energy and fluctuations. (a) Average energy per link as a function of the temperature T. The various curves correspond to different lengths of the zipper. In the thermodynamic limit, the average energy per link develops a discontinuity at the transition temperature Tc. (b) Variance of the energy for zippers of different lengths. The energy fluctuations diverge [45] at the transition temperature Tc in the thermodynamic limit.

Lee-Yang zeros for the zipper model. (a) Exact results for the leading Lee-Yang zeros in the complex plane of the inverse temperature for zippers of increasing size N=1,2,...,30. In the thermodynamic limit, the Lee-Yang zeros reach the inverse temperature on the real axis for which a phase transition occurs. The polar coordinates o and o defined in Eq. (16) are indicated. (b) Extrapolation of the real part and the imaginary part of the Lee-Yang zeros in the thermodynamic limit.

Extraction of Lee-Yang zeros from the energy cumulants. (a) The Lee-Yang zeros are extracted from four consecutive cumulants up to order nmax for zippers of length N=1,2,...,30. The inverse temperature is =0.75c. The inset illustrates how the accuracy of the method is improved by increasing the cumulant order. (b) Extrapolation of the real and imaginary parts of the Lee-Yang zeros in the thermodynamic limit. These results should be compared with the exact ones in Fig. 4.

Large-deviation statistics for the broken zipper. The inverse temperature is (a) =0.7Re[c], (b) =Re[c], and (c) =1.3Re[c], where Re[c] is the real part of the convergence points extracted in Fig. 6 with J=. The thick red lines are exact results based on Eq. (39) with N=103, while the blue lines are the top of the ellipse described by Eq. (48). The fitting parameters u1,u2, and N depend weakly on the temperature. The lower parts of the ellipses are indicated with dashed lines. ff782bc1db

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