The Vatican News App is an official mobile application software issued by the Vatican's Dicastery for Communication. Formerly titled The Pope App, the app was launched on January 23, 2013, under the auspices of the Pontifical Council for Social Communications, a now-defunct dicastery that was merged into the Secretariat (now Dicastery) for Communication in March 2016. Initially, The Pope App was available only on iOS devices, but became available for Android phones at the end of February 2013. The app is available for download on iOS and Android in five languages: English, French, Italian, Portuguese and Spanish. It was originally promoted as an application with focus on the figure of the Pope which made it possible to follow the Pope's events while they are taking place. Alerts notified the followers by informing and offering access to "official papal-related content in a variety of formats". The app also enabled its users to see areas of the Vatican through webcams allocated throughout St. Peter's Square in Rome that broadcast images. In early 2018, The Pope App was relaunched as the Vatican News App, accompanied by a redesign that eliminated many of the previous version's features, reducing the app to a more conventional news service, with increased emphasis on news from the Vatican and the worldwide Catholic Church and less focus on the day-to-day activities of the Pope.
Sentence embedding
In natural language processing, a sentence embedding is a representation of a sentence as a vector of numbers which encodes meaningful semantic information. State of the art embeddings are based on the learned hidden layer representation of dedicated sentence transformer models. BERT pioneered an approach involving the use of a dedicated [CLS] token prepended to the beginning of each sentence inputted into the model; the final hidden state vector of this token encodes information about the sentence and can be fine-tuned for use in sentence classification tasks. In practice however, BERT's sentence embedding with the [CLS] token achieves poor performance, often worse than simply averaging non-contextual word embeddings. SBERT later achieved superior sentence embedding performance by fine tuning BERT's [CLS] token embeddings through the usage of a siamese neural network architecture on the SNLI dataset. Other approaches are loosely based on the idea of distributional semantics applied to sentences. Skip-Thought trains an encoder-decoder structure for the task of neighboring sentences predictions; this has been shown to achieve worse performance than approaches such as InferSent or SBERT. An alternative direction is to aggregate word embeddings, such as those returned by Word2vec, into sentence embeddings. The most straightforward approach is to simply compute the average of word vectors, known as continuous bag-of-words (CBOW). However, more elaborate solutions based on word vector quantization have also been proposed. One such approach is the vector of locally aggregated word embeddings (VLAWE), which demonstrated performance improvements in downstream text classification tasks. == Applications == In recent years, sentence embedding has seen a growing level of interest due to its applications in natural language queryable knowledge bases through the usage of vector indexing for semantic search. LangChain for instance utilizes sentence transformers for purposes of indexing documents. In particular, an indexing is generated by generating embeddings for chunks of documents and storing (document chunk, embedding) tuples. Then given a query in natural language, the embedding for the query can be generated. A top k similarity search algorithm is then used between the query embedding and the document chunk embeddings to retrieve the most relevant document chunks as context information for question answering tasks. This approach is also known formally as retrieval-augmented generation. Though not as predominant as BERTScore, sentence embeddings are commonly used for sentence similarity evaluation which sees common use for the task of optimizing a Large language model's generation parameters is often performed via comparing candidate sentences against reference sentences. By using the cosine-similarity of the sentence embeddings of candidate and reference sentences as the evaluation function, a grid-search algorithm can be utilized to automate hyperparameter optimization. == Evaluation == A way of testing sentence encodings is to apply them on Sentences Involving Compositional Knowledge (SICK) corpus for both entailment (SICK-E) and relatedness (SICK-R). In the best results are obtained using a BiLSTM network trained on the Stanford Natural Language Inference (SNLI) Corpus. The Pearson correlation coefficient for SICK-R is 0.885 and the result for SICK-E is 86.3. A slight improvement over previous scores is presented in: SICK-R: 0.888 and SICK-E: 87.8 using a concatenation of bidirectional Gated recurrent unit.
Graph cuts in computer vision and artificial intelligence
As applied in the field of computer vision, graph cut optimization can be employed to efficiently solve a wide variety of low-level computer vision problems (early vision), such as image smoothing, the stereo correspondence problem, image segmentation, object co-segmentation, numerous military applications (eg Automatic target recognition) and many other problems that can be formulated in terms of energy minimization (eg Climate Science and Environmental modelling). Graph cut techniques are now increasingly being used in combination with more general spatial Artificial intelligence techniques (eg to enforce structure in Large language model output to sharpen tumour boundaries and similarly for various Augmented reality, Self-driving car, Robotics, Google Maps applications etc). Many of these energy minimization problems can be approximated by solving a maximum flow problem in a graph (and thus, by the max-flow min-cut theorem, define a minimal cut of the graph). Under most formulations of such problems in computer vision, the minimum energy solution corresponds to the maximum a posteriori estimate of a solution. Although many computer vision algorithms involve cutting a graph (e.g. normalized cuts), the term "graph cuts" is applied specifically to those models which employ a max-flow/min-cut optimization (other graph cutting algorithms may be considered as graph partitioning algorithms). "Binary" problems (such as denoising a binary image) can be solved exactly using this approach; problems where pixels can be labeled with more than two different labels (such as stereo correspondence, or denoising of a grayscale image) cannot be solved exactly, but solutions produced are usually near the global optimum. == History == The foundational theory of graph cuts in computer vision was first developed by Margaret Greig, Bruce Porteous and Allan Seheult (GPS) of Durham University in a now legendary discussion contribution to Julian Besag's 1986 paper and a more detailed follow on paper in 1989. In the Bayesian statistical context of smoothing noisy images, using a Markov random field as the image prior distribution, they showed with a mathematically beautiful proof how the maximum a posteriori estimate of a binary image can be obtained exactly by maximizing the flow through an associated image network, or graph, involving the introduction of a source and sink and Log-likelihood ratios. The problem was shown to be efficiently solvable exactly, an unexpected result as the problem was believed to be computationally intractable (NP hard). GPS also addressed the computational cost of the max-flow algorithm on large graphs, a significant concern at the time. They proposed a partitioning algorithm (see Section 4 of GPS) involving the recursive amalgamation of non-overlapping blocks, or tiles, which gave a 12X increase in speed. This approach recursively solved and amalgamated independent sub-graphs until the whole graph was solved. While contemporaries like Geman and Geman had advocated Parallel computing in the context of Simulated annealing, the GPS blocking strategy offered a deterministic structure amenable to parallelisation and anticipated modern artificial intelligence design across multiple GPUs. However, until recently, this aspect of the paper was largely ignored and subsequent research focused on Serial computer global search trees, such as the Boykov-Kolmogorov algorithm. Although the general k {\displaystyle k} -colour problem is NP hard for k > 2 , {\displaystyle k>2,} the GPS approach has turned out to have very wide applicability in general computer vision problems. This was first demonstrated by Boykov, Veksler and Zabih who, in a seminal paper published more than 10 years after the original GPS paper, and in other important works, lit the blue touch paper for the general adoption of graph cut techniques in computer vision. They showed that, for general problems, the GPS approach can be applied iteratively to sequences of binary problems, using their now ubiquitous alpha-expansion algorithm, yielding near optimal solutions. Prior to these results, approximate local optimisation techniques such as simulated annealing (as proposed by the Geman brothers) or iterated conditional modes (a type of greedy algorithm suggested by Julian Besag) were used to solve such image smoothing problems. Building on these advancements, GPS graph cut optimization was subsequently adapted for interactive image segmentation, most notably through the "GrabCut" algorithm introduced by Carsten Rother, Vladimir Kolmogorov, and Andrew Blake of Microsoft Research, Cambridge. GrabCut extended earlier interactive graph cut methods by replacing monochrome image histograms with Gaussian mixture models to estimate colour distributions, and by employing an iterative GPS energy minimisation scheme. This approach significantly simplified user interaction, requiring only a rough bounding box around the target object rather than detailed user-drawn strokes, and it quickly became a standard tool in both academic research and commercial image editing software. The GPS paper connected and bridged profound ideas from Mathematical statistics (Bayes' theorem, Markov random field), Physics (Ising model), Optimisation (Energy function) and Computer science (Network flow problem) and led the move away from approximate local and slow optimisation approaches (eg simulated annealing) to more powerful exact, or near exact, faster global optimisation techniques. It is now recognised as seminal as it was well ahead of its time and, in particular, was published years before the computing power revolution of Moore's law and GPUs. Significantly, GPS was published in a mathematical statistics (rather than a computer vision) journal, and this led to it being overlooked by the computer vision community for many years. It is unofficially known as "The Velvet Underground" paper of computer vision (ie although very few computer vision people read the paper [bought the record], those that did, most importantly Boykov, Veksler and Zabih, started new and important research [formed a band]). This is confirmed by GPS' very large amplification ratio (2nd order citations/first order citations), estimated at well in excess of 100. Despite the foundational nature of the GPS work, formal recognition from the computer vision community has predominantly gone to the researchers who followed to extend and popularise the graph cut method. For example, Boykov, Veksler and Zabih deservedly received a Helmholtz Prize from the ICCV in 2011. This prize recognises ICCV papers from 10 or more years earlier that have had a significant impact on computer vision research. In 2011, Couprie et al. proposed a general image segmentation framework, called the "Power Watershed", that minimized a real-valued indicator function from [0,1] over a graph, constrained by user seeds (or unary terms) set to 0 or 1, in which the minimization of the indicator function over the graph is optimized with respect to an exponent p {\displaystyle p} . When p = 1 {\displaystyle p=1} , the Power Watershed is optimized by graph cuts, when p = 0 {\displaystyle p=0} the Power Watershed is optimized by shortest paths, p = 2 {\displaystyle p=2} is optimized by the random walker algorithm and p = ∞ {\displaystyle p=\infty } is optimized by the watershed algorithm. In this way, the Power Watershed may be viewed as a generalization of graph cuts that provides a straightforward connection with other energy optimization segmentation/clustering algorithms. == Binary segmentation of images == === Notation === Image: x ∈ { R , G , B } N {\displaystyle x\in \{R,G,B\}^{N}} Output: Segmentation (also called opacity) S ∈ R N {\displaystyle S\in R^{N}} (soft segmentation). For hard segmentation S ∈ { 0 for background , 1 for foreground/object to be detected } N {\displaystyle S\in \{0{\text{ for background}},1{\text{ for foreground/object to be detected}}\}^{N}} Energy function: E ( x , S , C , λ ) {\displaystyle E(x,S,C,\lambda )} where C is the color parameter and λ is the coherence parameter. E ( x , S , C , λ ) = E c o l o r + E c o h e r e n c e {\displaystyle E(x,S,C,\lambda )=E_{\rm {color}}+E_{\rm {coherence}}} Optimization: The segmentation can be estimated as a global minimum over S: arg min S E ( x , S , C , λ ) {\displaystyle {\arg \min }_{S}E(x,S,C,\lambda )} === Existing methods === Standard Graph cuts: optimize energy function over the segmentation (unknown S value). Iterated Graph cuts: First step optimizes over the color parameters using K-means. Second step performs the usual graph cuts algorithm. These 2 steps are repeated recursively until convergence Dynamic graph cuts:Allows to re-run the algorithm much faster after modifying the problem (e.g. after new seeds have been added by a user). === Energy function === Pr ( x ∣ S ) = K − E {\displaystyle \Pr(x\mid S)=K^{-E}} where the energy E {\displaystyle E} is composed of two different mod
N-jet
An N-jet is the set of (partial) derivatives of a function f ( x ) {\displaystyle f(x)} up to order N. Specifically, in the area of computer vision, the N-jet is usually computed from a scale space representation L {\displaystyle L} of the input image f ( x , y ) {\displaystyle f(x,y)} , and the partial derivatives of L {\displaystyle L} are used as a basis for expressing various types of visual modules. For example, algorithms for tasks such as feature detection, feature classification, stereo matching, tracking and object recognition can be expressed in terms of N-jets computed at one or several scales in scale space.
Universal portfolio algorithm
The universal portfolio algorithm is a portfolio selection algorithm from the field of machine learning and information theory. The algorithm learns adaptively from historical data and maximizes log-optimal growth rate in the long run, per the Kelly criterion. It was introduced by the late Stanford University information theorist Thomas M. Cover. The algorithm rebalances the portfolio at the beginning of each trading period. At the beginning of the first trading period it starts with a naive diversification. In the following trading periods the portfolio composition depends on the historical total return of all possible constant-rebalanced portfolios. The universal portfolio algorithm is the predecessor of the various online portfolio selection methodologies.
Shearlet
In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Originally, shearlets were introduced in 2006 for the analysis and sparse approximation of functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . They are a natural extension of wavelets, to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, since wavelets, as isotropic objects, are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing, and translation applied to a few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads length² ≈ width. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} , they still form a frame allowing stable expansions of arbitrary functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . One of the most important properties of shearlets is their ability to provide optimally sparse approximations (in the sense of optimality in ) for cartoon-like functions f {\displaystyle f} . In imaging sciences, cartoon-like functions serve as a model for anisotropic features and are compactly supported in [ 0 , 1 ] 2 {\displaystyle [0,1]^{2}} while being C 2 {\displaystyle C^{2}} apart from a closed piecewise C 2 {\displaystyle C^{2}} singularity curve with bounded curvature. The decay rate of the L 2 {\displaystyle L^{2}} -error of the N {\displaystyle N} -term shearlet approximation obtained by taking the N {\displaystyle N} largest coefficients from the shearlet expansion is in fact optimal up to a log-factor: ‖ f − f N ‖ L 2 2 ≤ C N − 2 ( log N ) 3 , N → ∞ , {\displaystyle \|f-f_{N}\|_{L^{2}}^{2}\leq CN^{-2}(\log N)^{3},\quad N\to \infty ,} where the constant C {\displaystyle C} depends only on the maximum curvature of the singularity curve and the maximum magnitudes of f {\displaystyle f} , f ′ {\displaystyle f'} and f ″ . {\displaystyle f''.} This approximation rate significantly improves the best N {\displaystyle N} -term approximation rate of wavelets providing only O ( N − 1 ) {\displaystyle O(N^{-1})} for such class of functions. Shearlets are to date the only directional representation system that provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm that allows faithful implementation. Extensions of shearlet systems to L 2 ( R d ) , d ≥ 2 {\displaystyle L^{2}(\mathbb {R} ^{d}),d\geq 2} are also available. A comprehensive presentation of the theory and applications of shearlets can be found in. == Definition == === Continuous shearlet systems === The construction of continuous shearlet systems is based on parabolic scaling matrices A a = [ a 0 0 a 1 / 2 ] , a > 0 {\displaystyle A_{a}={\begin{bmatrix}a&0\\0&a^{1/2}\end{bmatrix}},\quad a>0} as a means to change the resolution, on shear matrices S s = [ 1 s 0 1 ] , s ∈ R {\displaystyle S_{s}={\begin{bmatrix}1&s\\0&1\end{bmatrix}},\quad s\in \mathbb {R} } as a means to change the orientation, and finally on translations to change the positioning. In comparison to curvelets, shearlets use shearings instead of rotations, the advantage being that the shear operator S s {\displaystyle S_{s}} leaves the integer lattice invariant in case s ∈ Z {\displaystyle s\in \mathbb {Z} } , i.e., S s Z 2 ⊆ Z 2 . {\displaystyle S_{s}\mathbb {Z} ^{2}\subseteq \mathbb {Z} ^{2}.} This indeed allows a unified treatment of the continuum and digital realm, thereby guaranteeing a faithful digital implementation. For ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} the continuous shearlet system generated by ψ {\displaystyle \psi } is then defined as SH c o n t ( ψ ) = { ψ a , s , t = a 3 / 4 ψ ( S s A a ( ⋅ − t ) ) ∣ a > 0 , s ∈ R , t ∈ R 2 } , {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )=\{\psi _{a,s,t}=a^{3/4}\psi (S_{s}A_{a}(\cdot -t))\mid a>0,s\in \mathbb {R} ,t\in \mathbb {R} ^{2}\},} and the corresponding continuous shearlet transform is given by the map f ↦ S H ψ f ( a , s , t ) = ⟨ f , ψ a , s , t ⟩ , f ∈ L 2 ( R 2 ) , ( a , s , t ) ∈ R > 0 × R × R 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(a,s,t)=\langle f,\psi _{a,s,t}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (a,s,t)\in \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} === Discrete shearlet systems === A discrete version of shearlet systems can be directly obtained from SH c o n t ( ψ ) {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )} by discretizing the parameter set R > 0 × R × R 2 . {\displaystyle \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} There are numerous approaches for this but the most popular one is given by { ( 2 j , k , A 2 j − 1 S k − 1 m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } ⊆ R > 0 × R × R 2 . {\displaystyle \{(2^{j},k,A_{2^{j}}^{-1}S_{k}^{-1}m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\}\subseteq \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} From this, the discrete shearlet system associated with the shearlet generator ψ {\displaystyle \psi } is defined by SH ( ψ ) = { ψ j , k , m = 2 3 j / 4 ψ ( S k A 2 j ⋅ − m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } , {\displaystyle \operatorname {SH} (\psi )=\{\psi _{j,k,m}=2^{3j/4}\psi (S_{k}A_{2^{j}}\cdot {}-m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\},} and the associated discrete shearlet transform is defined by f ↦ S H ψ f ( j , k , m ) = ⟨ f , ψ j , k , m ⟩ , f ∈ L 2 ( R 2 ) , ( j , k , m ) ∈ Z × Z × Z 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(j,k,m)=\langle f,\psi _{j,k,m}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (j,k,m)\in \mathbb {Z} \times \mathbb {Z} \times \mathbb {Z} ^{2}.} == Examples == Let ψ 1 ∈ L 2 ( R ) {\displaystyle \psi _{1}\in L^{2}(\mathbb {R} )} be a function satisfying the discrete Calderón condition, i.e., ∑ j ∈ Z | ψ ^ 1 ( 2 − j ξ ) | 2 = 1 , for a.e. ξ ∈ R , {\displaystyle \sum _{j\in \mathbb {Z} }|{\hat {\psi }}_{1}(2^{-j}\xi )|^{2}=1,{\text{for a.e. }}\xi \in \mathbb {R} ,} with ψ ^ 1 ∈ C ∞ ( R ) {\displaystyle {\hat {\psi }}_{1}\in C^{\infty }(\mathbb {R} )} and supp ψ ^ 1 ⊆ [ − 1 2 , − 1 16 ] ∪ [ 1 16 , 1 2 ] , {\displaystyle \operatorname {supp} {\hat {\psi }}_{1}\subseteq [-{\tfrac {1}{2}},-{\tfrac {1}{16}}]\cup [{\tfrac {1}{16}},{\tfrac {1}{2}}],} where ψ ^ 1 {\displaystyle {\hat {\psi }}_{1}} denotes the Fourier transform of ψ 1 . {\displaystyle \psi _{1}.} For instance, one can choose ψ 1 {\displaystyle \psi _{1}} to be a Meyer wavelet. Furthermore, let ψ 2 ∈ L 2 ( R ) {\displaystyle \psi _{2}\in L^{2}(\mathbb {R} )} be such that ψ ^ 2 ∈ C ∞ ( R ) , {\displaystyle {\hat {\psi }}_{2}\in C^{\infty }(\mathbb {R} ),} supp ψ ^ 2 ⊆ [ − 1 , 1 ] {\displaystyle \operatorname {supp} {\hat {\psi }}_{2}\subseteq [-1,1]} and ∑ k = − 1 1 | ψ ^ 2 ( ξ + k ) | 2 = 1 , for a.e. ξ ∈ [ − 1 , 1 ] . {\displaystyle \sum _{k=-1}^{1}|{\hat {\psi }}_{2}(\xi +k)|^{2}=1,{\text{for a.e. }}\xi \in \left[-1,1\right].} One typically chooses ψ ^ 2 {\displaystyle {\hat {\psi }}_{2}} to be a smooth bump function. Then ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} given by ψ ^ ( ξ ) = ψ ^ 1 ( ξ 1 ) ψ ^ 2 ( ξ 2 ξ 1 ) , ξ = ( ξ 1 , ξ 2 ) ∈ R 2 , {\displaystyle {\hat {\psi }}(\xi )={\hat {\psi }}_{1}(\xi _{1}){\hat {\psi }}_{2}\left({\tfrac {\xi _{2}}{\xi _{1}}}\right),\quad \xi =(\xi _{1},\xi _{2})\in \mathbb {R} ^{2},} is called a classical shearlet. It can be shown that the corresponding discrete shearlet system SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} constitutes a Parseval frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} consisting of bandlimited functions. Another example are compactly supported shearlet systems, where a compactly supported function ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} can be chosen so that SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} forms a frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} . In this case, all shearlet elements in SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} are compactly supported providing superior spatial localization compared to the classical shearlets, which are bandlimited. Although a compactly supported shearlet system does not generally form a Parseval frame, any function f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} can be represented by the shearlet expansion due to its frame property. == Cone-adapted shearlets == One drawback of shearlets defined as above is the directional bias of shearlet elements associated with large shearing parameters. This effect is already r
Transderivational search
Transderivational search (often abbreviated to TDS) is a psychological and cybernetics term, meaning when a search is being conducted for a fuzzy match across a broad field. In computing the equivalent function can be performed using content-addressable memory. Unlike usual searches, which look for literal (i.e. exact, logical, or regular expression) matches, a transderivational search is a search for a possible meaning or possible match as part of communication, and without which an incoming communication cannot be made any sense of whatsoever. It is thus an integral part of processing language, and of attaching meaning to communication. In NLP (Neuro-linguistic programming), a transderivational search (Bandler and Grinder, 1976) is essentially the process of searching back through one's stored memories and mental representations to find the personal reference experiences from which a current understanding or mental map has been derived. By the end of 1976, Grinder and Bandler had combined Satir’s and Perls’ language patterns and Erickson’s hypnotic language and use of metaphor with anchoring to create new processes that they called collapsing anchors, trans-derivational search, changing personal history, and reframing. A psychological example of TDS is in Ericksonian hypnotherapy, where vague suggestions are used that the patient must process intensely in order to find their own meanings, thus ensuring that the practitioner does not intrude his own beliefs into the subject's inner world. == TDS in human communication and processing == Because TDS is a compelling, automatic and unconscious state of internal focus and processing (i.e. a type of everyday trance state), and often a state of internal lack of certainty, or openness to finding an answer (since something is being checked out at that moment), it can be utilized or interrupted, in order to create, or deepen, trance. TDS is a fundamental part of human language and cognitive processing. Arguably, every word or utterance a person hears, for example, and everything they see or feel and take note of, results in a very brief trance while TDS is carried out to establish a contextual meaning for it. === Examples === Leading statements: "And those thoughts you had yesterday..." the human mind cannot process hearing this phrase, without at some level searching internally for some thoughts or other that it had yesterday, to make the subject of the sentence. "The many colors that fruit can be" likewise starts the human mind considering even if briefly, different fruit sorted by color. "You did it again, didn't you!" This everyday manipulative use of TDS usually sends the recipient looking internally for some "it" they may have done for which blame is being fairly given. Regardless of whether such a matter can be identified, guilt or anger may result. "There has been pain, hasn't there" the mind of a patient suffering an illness will find it very hard or impossible to hear or answer this sentence without conducting internal searches to verify whether this is true or not, or to find an example if so. "You'd forgotten something [or: some part of your body], hadn't you?" the mind usually checks through the various things, or parts of the body, on hearing this, seeing if each in turn has been forgotten. Textual ambiguity: "Do you remember line dancing on the steps?" Without sufficient context, some statements may trigger TDS in order to resolve inherent ambiguity in the interpretation of a posed question. Do I remember a bygone fad called "line dancing on the steps"? Do I remember personally engaging in dancing in the past? Do I remember my routine practice dancing by focusing on the steps of the dance? Do I tend to forget about dancing when I am standing on steps? "Penny-wise and pound the table dance to the beat of a different drummer". The mixing of cliché and stock phrases may trigger TDS in order to reconcile the discrepancies between expected and actual utterances in sequence. Although TDS is often associated with spoken language, it can be induced in any perceptual system. Thus Milton Erickson's "hypnotic handshake" is a technique that leaves the other person performing TDS in search of meaning to a deliberately ambiguous use of touch.